#1. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:
A. 45 : 56
B. 45 : 51
C. 47 : 56
D. 47 : 51
Answer: Option A Solution: Let: – \( CP \) = Cost Price of the book – \( MP \) = Marked (Printed) Price of the book – \( SP \) = Selling Price of the book
Step 1: Express Selling Price in Terms of Marked Price Since the book is sold at a **10% discount** on the printed price: \[ SP = MP \times \left(1 – \frac{10}{100}\right) = MP \times 0.9 \]
Step 2: Express Cost Price in Terms of Selling Price The shopkeeper earns a **12% profit** on the cost price: \[ SP = CP \times \left(1 + \frac{12}{100}\right) = CP \times 1.12 \]
Step 3: Equate Both Expressions for Selling Price \[ CP \times 1.12 = MP \times 0.9 \]
Step 4: Find the Ratio \( CP : MP \) \[ \frac{CP}{MP} = \frac{0.9}{1.12} \]
\[ = \frac{90}{112} = \frac{45}{56} \]
Thus, the ratio of cost price to printed price is \( 45:56 \).
#2. By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:
A. Rs. 2600
B. Rs. 2700
C. Rs. 2800
D. Rs. 3000
Answer: Option B Solution: Given Data: – Selling Price (SP) at 14% profit = Rs. 2850 – Profit Percentage = 14% – New Profit Percentage = 8%
Step 1: Find Cost Price (CP) We use the formula: \[ SP = CP \times \left(1 + \frac{\text{Profit \%}}{100} \right) \]
Step 2: Find New Selling Price at 8% Profit \[ SP’ = CP \times \left(1 + \frac{8}{100} \right) \]
\[ SP’ = 2500 \times 1.08 \]
\[ SP’ = 2700 \]
Answer: The new selling price will be Rs. 2700.
#3. A sells an article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction:
A. A neither losses nor gains
B. A makes a profit of 11%
C. A makes a profit of 20%
D. B loses 20%
Answer: Option B Solution: First Method Let CP was 100 for A originally A sells article to B at 10% profit, CP for B = 100 + 10% of 100 = 110 Now, B sells it A again with loss 10% Now, CP for A this time = 110 – 10% of 110 = 99 A makes Profit = 110 – 99 = 11 %profit for A =\( \frac{11 × 100}{100} \) = 11% Second Method It could be easily shown by net percentage change graphic. 100(A) == 10%(Profit) ⇒110(B) == 10%(Loss) ⇒ 99(A) In this transaction A makes a profit of (110 – 99 = 11%) 11% [10% on selling to B and 1% profit on buying back from B]
#4. A person sold a horse at a gain of 15%. Had he bought it for 25% less and sold it for Rs. 600 less, he would have made a profit of 32%. The cost price of the horse was:
A. Rs. 3,750
B. Rs. 3,250
C. Rs. 2,750
D. Rs. 2,250
Answer: Option A Solution: Let the original cost price of the horse be Rs. \( x \).
Step 1: Express the Selling Price in Terms of \( x \) Since the horse was sold at a 15% profit, the selling price (SP) is:
\[ SP = x + 15\% \text{ of } x = x \times 1.15 \]
Step 2: Express the New Cost Price and Selling Price If the person had **bought it for 25% less**, the new cost price would be:
\[ CP’ = x – 25\% \text{ of } x = x \times 0.75 \]
If he had sold it for Rs. 600 less than before, the new selling price would be:
\[ SP’ = SP – 600 = 1.15x – 600 \]
He would have made a 32% profit** on the new cost price:
\[ SP’ = CP’ \times 1.32 \]
Step 3: Set Up the Equation \[ 1.15x – 600 = 0.75x \times 1.32 \]
\[ 1.15x – 600 = 0.99x \]
\[ 1.15x – 0.99x = 600 \]
\[ 0.16x = 600 \]
\[ x = \frac{600}{0.16} = 3750 \]
Final Answer: The original cost price of the horse was Rs. 3750.
#5. If a man were to sell his chair for Rs. 720, he would lose 25%. To gain 25% he should sell it for:
A. Rs. 1,200
B. Rs. 1,000
C. Rs. 960
D. Rs. 900
Answer: Option A Solution: Given Data: – Selling Price (SP) at 25% loss = Rs. 720 – Loss Percentage = 25% – We need to find the new SP to make a 25% profit.
Step 1: Find Cost Price (CP) Using the loss formula:
Answer: To gain 25% profit, he should sell the chair for Rs. 1200.
#6. A man sold two chairs at Rs. 1200 each. On one he gained 20% and on the other he loss 20%. His gain or loss in the whole transaction is:
A. 1% loss
B. 2% loss
C. 4% loss
D. 15 gain
Answer: Option C Solution: This problem involves equal selling prices but different profit and loss percentages, which leads to an overall loss.
Given Data: – Selling Price (SP) of each chair = Rs. 1200 – Profit on one chair = 20% – Loss on the other chair = 20%
Step 1: Find Cost Prices of Both Chairs First Chair (20% Gain) Let Cost Price (CP₁) be \( x \), then:
#8. If the profit per cent got on selling an article is numerically equal to its cost price in rupees and the selling price is Rs. 39, then cost price (in Rs.) will be:
A. 20
B. 22
C. 28
D. 30
Answer: Option D Solution: Given Data: – Let Cost Price (CP) = x rupees. – Profit percentage is numerically equal to the cost price, i.e., Profit % = x. – Selling Price (SP) = **Rs. 39**. – Using the profit formula:
\[ 39 = x \times \left(1 + \frac{x}{100} \right) \]
Step 1: Solve for \( x \)
\[ 39 = x + \frac{x^2}{100} \]
\[ 39 \times 100 = 100x + x^2 \]
\[ 3900 = x^2 + 100x \]
\[ x^2 + 100x – 3900 = 0 \]
Step 2: Solve the Quadratic Equation The quadratic equation is:
\[ x^2 + 100x – 3900 = 0 \]
Using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \]
where a = 1, b = 100, and c = -3900.
\[ x = \frac{-100 \pm \sqrt{100^2 – 4(1)(-3900)}}{2(1)} \]
\[ x = \frac{-100 \pm \sqrt{10000 + 15600}}{2} \]
\[ x = \frac{-100 \pm \sqrt{25600}}{2} \]
\[ x = \frac{-100 \pm 160}{2} \]
Step 3: Find the Valid Value of \( x \) \[ x = \frac{-100 + 160}{2} = \frac{60}{2} = 30 \]
(Negative value is not possible for cost price)
Final Answer: The cost price is Rs. 30.
#9. A man buys a field of agricultural land for Rs. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?
A. Rs.1,00,000
B. Rs. 1,15,000
C. Rs. 1,20,000
D. Rs. 1,25,000
Answer: Option C Solution: Given Data: – Total cost price (CP) of the field = Rs. 3,60,000. – The man sells: – One-third of the land at a loss of 20%. – Two-fifths of the land at a gain of 25%. – The remaining portion of the land is to be sold at a price that ensures an overall profit of 10%.
Step 1: Total Land Area Calculation Let the total area of the field be represented by A.
– Cost price per unit area = \( \frac{3,60,000}{A} \).
Step 2: Selling One-Third at a Loss of 20% The area sold at a loss of 20% is one-third of the total field:
\[ \text{Area sold at a loss} = \frac{1}{3} A \] The cost price of this portion is:
Final Answer: The man must sell the remaining field for Rs. 1,20,000** to make an overall profit of 10%.
#10. An article is listed at Rs. 920. A customer pays Rs. 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is:
A. 3%
B. 5%
C. 8%
D. 12%
Answer: Option B Solution: Given Data: – Listed Price (MP) = Rs. 920 – Selling Price after discounts (SP) = Rs. 742.90 – First discount = 15% – We need to find the second discount rate.
Step 1: Apply the First Discount Let the first discount rate be 15%.
The price after the first discount:
\[ \text{Price after first discount} = MP \times (1 – \frac{15}{100}) = 920 \times 0.85 = 782 \]
So, after the first discount, the price is **Rs. 782**.
Step 2: Apply the Second Discount Let the second discount rate be x%. After applying the second discount, the final price is Rs. 742.90.
Final Answer: The second discount rate is approximately 5%.
#11. A tradesman marks his goods at 25% above the cost price and allows purchasers a discount of\( \frac{25}{2} \) %, his profit is:
A. 8%
B. 8.5%
C. 8.625%
D. 9.375%
Answer: Option D Solution Let’s solve this step by step.
– Let the cost price of the goods be \( C \). – The tradesman marks the goods at 25% above the cost price. Therefore, the marked price (MP) is:
\[ MP = C + 0.25C = 1.25C \]
– The tradesman allows a discount of \( \frac{25}{2} \% \), which is 12.5% on the marked price. The selling price (SP) is:
#12. A bicycle marked at Rs. 2,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:
A. Rs. 1,368
B. Rs. 1,468
C. Rs. 1,568
D. Rs. 1,668
Answer: Option A Solution: Let’s solve this step by step.
1. Marked Price (MP) of the bicycle is Rs. 2000.
2. First Discount of 20%: – After applying the first discount, the price becomes: \[ \text{Price after first discount} = 2000 – 20\% \text{ of } 2000 = 2000 – 0.20 \times 2000 = 2000 – 400 = 1600 \]
3. Second Discount of 10%: – After applying the second discount, the price becomes: \[ \text{Price after second discount} = 1600 – 10\% \text{ of } 1600 = 1600 – 0.10 \times 1600 = 1600 – 160 = 1440 \]
4. Additional Cash Discount of 5%: – After applying the 5% discount for cash payment, the final price becomes: \[ \text{Price after cash discount} = 1440 – 5\% \text{ of } 1440 = 1440 – 0.05 \times 1440 = 1440 – 72 = 1368 \]
So, the selling price of the bicycle with the cash discount is Rs. 1368.
#13. The marked price of a shirt and trousers are in the ratio 1:2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:
A. 15%
B. 20%
C. 25%
D. 30%
Answer: Option C Solution: Let’s solve this step by step.
Step 1: Let the marked price of the shirt and trousers be in the ratio 1:2. – Let the marked price of the shirt be \( x \). – Therefore, the marked price of the trousers is \( 2x \).
Step 2: Discount on the shirt. – The shopkeeper gives a 40% discount on the shirt, so the selling price of the shirt after the discount is: \[ \text{Selling price of the shirt} = x – 0.40 \times x = 0.60x \]
Step 3: Discount on the trousers. – Let the discount offered on the trousers be \( y \% \). So, the selling price of the trousers after the discount is: \[ \text{Selling price of the trousers} = 2x – \frac{y}{100} \times 2x = 2x \left( 1 – \frac{y}{100} \right) \]
Step 4: Total discount on the set of shirt and trousers. – The total marked price of the shirt and trousers together is: \[ \text{Total marked price} = x + 2x = 3x \] – The total selling price after the discounts is: \[ \text{Total selling price} = 0.60x + 2x \left( 1 – \frac{y}{100} \right) \] – The total discount is the difference between the total marked price and the total selling price: \[ \text{Total discount} = 3x – \left( 0.60x + 2x \left( 1 – \frac{y}{100} \right) \right) \] – The total discount percentage is given as 30%. So, the total discount is also: \[ \text{Total discount} = 30\% \text{ of } 3x = 0.30 \times 3x = 0.90x \]
Step 5: Set up the equation. Now, we can set up the equation for the total discount: \[ 3x – \left( 0.60x + 2x \left( 1 – \frac{y}{100} \right) \right) = 0.90x \]
Step 6: Solve for \( y \). Now divide both sides of the equation by \( 2x \): \[ \frac{y}{100} = \frac{0.50x}{2x} \] \[ \frac{y}{100} = 0.25 \] \[ y = 25 \]
Conclusion: The discount offered on the trousers is 25%.
#14. A dealer buys an article marked at Rs. 25,000 with 20% and 5% off. He spends Rs. 1,000 for its repairs and sells it for Rs. 25,000. What is his gain or loss per cent?
A. loss of 25%
B. gain of 25%
C. gain 10%
D. loss of 10%
Answer: Option B Solution: Let’s break this down step by step:
Step 1: Calculate the cost price of the article. The dealer buys the article marked at Rs. 25,000, but he gets two successive discounts of 20% and 5%.
1. First Discount (20%): \[ \text{Price after 20% discount} = 25000 – 20\% \text{ of } 25000 = 25000 – 0.20 \times 25000 = 25000 – 5000 = 20000 \]
2. Second Discount (5%): \[ \text{Price after 5% discount} = 20000 – 5\% \text{ of } 20000 = 20000 – 0.05 \times 20000 = 20000 – 1000 = 19000 \]
So, the cost price of the article after both discounts is Rs. 19,000.
Step 2: Add the repair cost. The dealer spends Rs. 1,000 for repairs. Therefore, the total cost price (including repairs) is: \[ \text{Total cost price} = 19000 + 1000 = 20000 \]
Step 3: Selling Price. The dealer sells the article for Rs. 25,000.
Step 4: Calculate the gain. The gain is the difference between the selling price and the total cost price: \[ \text{Gain} = 25000 – 20000 = 5000 \]
Step 5: Calculate the gain percentage. The gain percentage is calculated as: \[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{Total Cost Price}} \right) \times 100 = \left( \frac{5000}{20000} \right) \times 100 = 25\% \]
Conclusion: The dealer’s gain is 25%.
#15. A trader sells his goods at a discount 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be:
A. 56.25%
B. 25.56%
C. 50.25%
D. 54.25%
Answer: Option A Solution: Let’s solve this step by step.
Step 1: Define the variables – Let the cost price (C.P.) of the goods be \( C \). – Let the marked price (M.P.) of the goods be \( M \). – The trader gives a 20% discount on the marked price.
Step 2: Selling price after discount Since the trader gives a 20% discount on the marked price, the selling price (S.P.) after the discount is: \[ S.P. = M – 20\% \text{ of } M = 0.80M \]
Step 3: Profit with 25% The trader still makes a profit of 25%, which means: \[ S.P. = C + 25\% \text{ of } C = 1.25C \]
So, we know: \[ 0.80M = 1.25C \]
Step 4: Find the marked price in terms of the cost price From the above equation: \[ M = \frac{1.25C}{0.80} = 1.5625C \]
Step 5: Selling at the marked price If the trader sells the goods at the marked price (without any discount), the selling price is \( M \). So, the profit will be: \[ \text{Profit} = M – C = 1.5625C – C = 0.5625C \]
Conclusion: If the trader sells the goods at the marked price, his profit will be 56.25%.
#16. The marked price of a radio is 20% more than its cost price. If a discount of 10% is given on the marked price, the gain per cent is:
A. 15
B. 12
C. 10
D. 8
Answer: Option D Solution: Let’s solve this step by step:
Step 1: Define the variables – Let the cost price (C.P.) of the radio be \( C \). – The marked price (M.P.) of the radio is 20% more than its cost price, so: \[ M.P. = C + 20\% \text{ of } C = 1.20C \]
Step 2: Selling price after discount A discount of 10% is given on the marked price, so the selling price (S.P.) after the discount is: \[ S.P. = M.P. – 10\% \text{ of } M.P. = 1.20C – 0.10 \times 1.20C = 1.20C \times 0.90 = 1.08C \]
Step 3: Calculate the gain The gain is the difference between the selling price and the cost price: \[ \text{Gain} = S.P. – C = 1.08C – C = 0.08C \]
Step 4: Calculate the gain percentage The gain percentage is: \[ \text{Gain Percentage} = \frac{\text{Gain}}{C} \times 100 = \frac{0.08C}{C} \times 100 = 8\% \]
Conclusion: The gain percentage is 8%.
#17. A shopkeeper sells sugar in such a way that the selling price of 950g of sugar is the same s the cost price of 1 kg of sugar. What is his gain percent?
A. 5.26%
B. 5\( \frac{1}{5} \)
C. 5 %
D. 4\( \frac{1}{19} \)
Answer: Option A Solution: Let’s break this down step by step:
Step 1: Define the variables – Let the cost price of 1 kg (1000g) of sugar be \( C \). – Therefore, the cost price of 950g of sugar is \( \frac{950}{1000} \times C = 0.95C \).
Step 2: Selling price of 950g of sugar The shopkeeper sells 950g of sugar at the same price as the cost price of 1 kg (1000g) of sugar. So, the selling price (S.P.) of 950g of sugar is \( C \).
Step 3: Calculate the gain The gain is the difference between the selling price and the cost price of 950g of sugar: \[ \text{Gain} = S.P. – \text{Cost price of 950g} = C – 0.95C = 0.05C \]
Step 4: Calculate the gain percentage The gain percentage is calculated based on the cost price of 950g of sugar (which is \( 0.95C \)): \[ \text{Gain Percentage} = \frac{\text{Gain}}{\text{Cost price of 950g}} \times 100 = \frac{0.05C}{0.95C} \times 100 \]
Conclusion: The shopkeeper’s gain percentage is approximately 5.26%.
#18. After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark on his goods?
A. 28.56%
B. 35%
C. 22.22%
D. None of these
Answer: Option A Solution: Let’s solve this step by step.
Step 1: Define the variables – Let the cost price (C.P.) of the goods be \( C \). – Let the marked price (M.P.) of the goods be \( M \).
Step 2: Selling price after discount The trader allows a discount of 11.11%, so the selling price (S.P.) after the discount is: \[ S.P. = M – 11.11\% \text{ of } M = M – 0.1111 \times M = 0.8889M \]
Step 3: Selling price and gain The trader still makes a gain of 14.28%, which means the selling price is 14.28% more than the cost price. So, the selling price is: \[ S.P. = C + 14.28\% \text{ of } C = 1.1428C \]
Step 4: Equating the two expressions for selling price Now, we can equate the two expressions for the selling price: \[ 0.8889M = 1.1428C \]
Step 5: Solve for the marked price Rearranging the above equation to solve for \( M \): \[ M = \frac{1.1428C}{0.8889} = 1.2857C \]
Step 6: Calculate the percentage markup The marked price is \( 1.2857C \), meaning the goods are marked at 28.57% above the cost price.
Conclusion: The trader marks his goods at 28.57% above the cost price.
#19. A dealer buys dry fruits at Rs. 100, Rs. 80, and Rs. 60 per kilogram. He mixes them in the ratio 3:4:5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruits?
A. Rs. 80
B. Rs. 100
C. Rs. 95
D. None of these
Answer: Option D Solution: Let’s solve this step by step.
Step 1: Calculate the cost price per kilogram of the mixed dry fruits The dealer mixes the dry fruits in the ratio 3:4:5 by weight. We will calculate the cost price (C.P.) per kilogram for the mixed dry fruits.
– The cost price of 1 kg of the first dry fruit is Rs. 100. – The cost price of 1 kg of the second dry fruit is Rs. 80. – The cost price of 1 kg of the third dry fruit is Rs. 60.
Since the ratio is 3:4:5, the total weight of the mix is \( 3 + 4 + 5 = 12 \) parts.
Now, calculate the total cost for the mixed 12 parts:
\[ \text{Total cost of the mix} = (3 \times 100) + (4 \times 80) + (5 \times 60) \] \[ \text{Total cost of the mix} = 300 + 320 + 300 = 920 \]
The cost price per kilogram of the mix is: \[ \text{C.P. per kg of the mix} = \frac{920}{12} = 76.67 \, \text{Rs. per kg} \]
Step 2: Calculate the selling price The dealer sells the mix at a profit of 50%. The selling price (S.P.) is calculated as: \[ \text{S.P. per kg} = \text{C.P. per kg} \times (1 + \text{Profit Percentage}) \] \[ \text{S.P. per kg} = 76.67 \times (1 + 0.50) = 76.67 \times 1.50 = 115 \, \text{Rs. per kg} \]
Conclusion: The dealer sells the mixed dry fruits at Rs. 115 per kilogram.
#20. The cost price of an article is 80% of its marked price for sale. How much per cent does the tradesman gain after allowing a discount of 12%?
A. 20%
B. 12%
C. 10%
D. 8%
Answer: Option C Solution: Let’s solve this step by step.
Step 1: Define the variables – Let the marked price (M.P.) of the article be \( M \). – The cost price (C.P.) is 80% of the marked price, so: \[ C.P. = 0.80M \]
Step 2: Selling price after discount The tradesman allows a discount of 12%, so the selling price (S.P.) is: \[ S.P. = M – 12\% \text{ of } M = 0.88M \]
Step 3: Calculate the gain The gain is the difference between the selling price and the cost price: \[ \text{Gain} = S.P. – C.P. = 0.88M – 0.80M = 0.08M \]
Step 4: Calculate the gain percentage The gain percentage is calculated based on the cost price: \[ \text{Gain Percentage} = \frac{\text{Gain}}{C.P.} \times 100 = \frac{0.08M}{0.80M} \times 100 = \frac{0.08}{0.80} \times 100 = 10\% \]
Conclusion: The tradesman gains 10% after allowing a discount of 12%.
#21. A merchant has announced 25% rebate on prices of ready-made garments at the time of sale. If a purchaser needs to have a rebate of Rs. 400, then how many shirts, each costing Rs. 320, should he purchase?
A. 10
B. 7
C. 6
D. 5
Answer: Option D Solution: Let’s solve this step by step.
Step 1: Define the variables – The cost of each shirt is Rs. 320. – The merchant is offering a 25% rebate on the prices of ready-made garments.
Step 2: Calculate the rebate on one shirt The rebate on one shirt is 25% of Rs. 320: \[ \text{Rebate on one shirt} = 25\% \times 320 = 0.25 \times 320 = 80 \, \text{Rs.} \]
Step 3: Determine the number of shirts needed The total rebate required is Rs. 400. To find out how many shirts need to be purchased, divide the total rebate by the rebate on one shirt: \[ \text{Number of shirts} = \frac{\text{Total rebate}}{\text{Rebate per shirt}} = \frac{400}{80} = 5 \]
Conclusion: The purchaser should buy 5 shirts to get a rebate of Rs. 400.
#22. A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea?
A. Rs. 70
B. Rs. 80
C. Rs. 90
D. Rs. 100
Answer: Option C Solution: Let’s solve this step by step.
Step 1: Define the variables – Let the original price per kg of tea be \( P \). – The new price after a 10% reduction is \( 0.90P \). – The dealer spends Rs. 22,500 to purchase tea.
Step 2: Number of kilograms purchased before and after the reduction – Before the reduction, the dealer buys tea at the original price. The amount of tea purchased with Rs. 22,500 is: \[ \text{Amount of tea before reduction} = \frac{22500}{P} \]
– After the reduction, the dealer buys tea at the reduced price \( 0.90P \). The amount of tea purchased after the reduction is: \[ \text{Amount of tea after reduction} = \frac{22500}{0.90P} = \frac{22500}{0.9P} = \frac{25000}{P} \]
Step 3: The difference in the amount of tea The dealer purchases 25 kg more tea after the reduction, so: \[ \frac{25000}{P} – \frac{22500}{P} = 25 \]
Step 4: Solve for \( P \) \[ P = \frac{2500}{25} = 100 \]
Step 5: Find the reduced price per kg The reduced price is 10% less than the original price, so: \[ \text{Reduced price} = 0.90 \times 100 = 90 \]
Conclusion: The reduced price per kg of tea is Rs. 90.
#23. A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Rs. 330 for it, how much did it cost to A?
A. Rs. 200
B. Rs. 250
C. Rs. 275
D. Rs. 290
Answer: Option A Solution: Let’s solve this step by step.
Step 1: Define the variables Let the cost price of the article to A be \( x \).
Step 2: Calculate the price at each transaction – A sells the article to B at a gain of 25%. Therefore, the price at which A sells to B is: \[ \text{Price from A to B} = x + 25\% \times x = 1.25x \]
– B sells it to C at a gain of 20%. Therefore, the price at which B sells to C is: \[ \text{Price from B to C} = 1.25x + 20\% \times 1.25x = 1.25x \times 1.20 = 1.5x \]
– C sells it to D at a gain of 10%. Therefore, the price at which C sells to D is: \[ \text{Price from C to D} = 1.5x + 10\% \times 1.5x = 1.5x \times 1.10 = 1.65x \]
Step 3: Price paid by D We know that D pays Rs. 330 for the article, so: \[ 1.65x = 330 \]
Step 4: Solve for \( x \) \[ x = \frac{330}{1.65} = 200 \]
Conclusion: The cost price to A was Rs. 200.
#24. I sold two watches for Rs. 300 each, one at loss of 20% and other at the profit of 20%. What is the percentage of loss (-) or profit (+) that resulted from the transaction?
A. (+)4
B. (-)1
C. (+)1
D. (-)4
Answer: Option D Solution: Let’s solve this step by step:
Step 1: Define the cost prices for the two watches – Let the cost price of the first watch (sold at a loss of 20%) be \( C_1 \). – Let the cost price of the second watch (sold at a profit of 20%) be \( C_2 \).
Step 2: Calculate the cost price of the first watch The first watch was sold for Rs. 300 at a loss of 20%. The cost price \( C_1 \) can be calculated as: \[ \text{Selling Price} = \text{Cost Price} – 20\% \times \text{Cost Price} \] \[ 300 = C_1 – 0.20 \times C_1 = 0.80 \times C_1 \] \[ C_1 = \frac{300}{0.80} = 375 \]
Step 3: Calculate the cost price of the second watch The second watch was sold for Rs. 300 at a profit of 20%. The cost price \( C_2 \) can be calculated as: \[ \text{Selling Price} = \text{Cost Price} + 20\% \times \text{Cost Price} \] \[ 300 = C_2 + 0.20 \times C_2 = 1.20 \times C_2 \] \[ C_2 = \frac{300}{1.20} = 250 \]
Step 4: Calculate the total cost price and total selling price – The total cost price is \( C_1 + C_2 = 375 + 250 = 625 \). – The total selling price is \( 300 + 300 = 600 \).
Step 5: Calculate the overall profit or loss The total loss is: \[ \text{Loss} = \text{Total Cost Price} – \text{Total Selling Price} = 625 – 600 = 25 \]
Step 6: Calculate the percentage of loss The percentage of loss is: \[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{Total Cost Price}} \times 100 = \frac{25}{625} \times 100 = 4\% \]
Conclusion: The overall result is a loss of 4% from the transaction.
#25. A shopkeeper wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10%. If his cost price is Rs. 95, then marked price is:
A. Rs. 100
B. Rs.110
C. Rs. 120
D. Rs. 130
Answer: Option B Solution: Let’s solve this step by step.
Step 1: Define the variables – Let the cost price (C.P.) of the article be Rs. 95. – Let the marked price (M.P.) be \( M \).
Step 2: Calculate the selling price The shopkeeper wants to earn a profit of 10%. The selling price (S.P.) can be calculated as: \[ S.P. = C.P. + 10\% \times C.P. = 95 + 0.10 \times 95 = 95 + 9.5 = 104.5 \]
Step 3: Calculate the commission The shopkeeper gives a 5% commission on the marked price. If \( M \) is the marked price, the commission is: \[ \text{Commission} = 5\% \times M = 0.05M \]
Step 4: Determine the relationship between selling price, marked price, and commission The selling price is the marked price minus the commission: \[ S.P. = M – 0.05M = 0.95M \]
Step 5: Equate the selling price and solve for the marked price We know the selling price is Rs. 104.5, so: \[ 0.95M = 104.5 \] \[ M = \frac{104.5}{0.95} = 110 \]
Conclusion: The marked price of the article is Rs. 110.
#26. Two successive discount of 10% and 20% are equivalent to a single discount of:
A. 30%
B. 28%
C. 26%
D. 25%
Answer: Option B Solution: To find the single discount equivalent to two successive discounts of 10% and 20%, we can use the formula:
Therefore, the single discount equivalent to two successive discounts of 10% and 20% is 28%.
This means that applying a single 28% discount results in the same final price as applying a 10% discount followed by a 20% discount.
#27. A dealer allows his customer a discount of 25% and still gains 25%. If cost price of a radio is Rs. 1440, its marked price is:
A. Rs. 2500
B. Rs. 2440
C. Rs. 2400
D. Rs. 2020
Answer: Option C Solution: To determine the marked price of the radio, let’s break down the problem step by step:
Substitute the known selling price into the equation:
\[ 1,800 = 0.75 \times \text{M.P.} \]
Solving for M.P.:
\[ \text{M.P.} = \frac{1,800}{0.75} = 2,400 \]
Conclusion:
The marked price of the radio is Rs. 2,400.
#28. The selling price of an article after giving two successive discounts of 10% and 5% on the marked price is Rs. 171. What is the marked price?
A. Rs. 200
B. Rs. 220
C. Rs. 240
D. Rs. 250
Answer: Option A Solution: To determine the marked price of the article, let’s break down the problem step by step:
Given: – Selling Price (S.P.): Rs. 171 – First Discount:10% – Second Discount: 5%
Step 1: Understand Successive Discounts
When two successive discounts are applied, the overall effect is equivalent to a single discount. The formula to calculate the overall discount percentage is:
#29. A man purchased some fruits for Rs. 1000. He sold few fruits worth 400 at 10% profit. At what profit per cent, must he sell the rest in order to gain 20% on the whole?
A. 26.67%
B. 25%
C. 30%
D. 33\( \frac{1}{3} \)
Answer: Option A Solution: To determine the profit percentage required on the remaining fruits to achieve an overall 20% profit, let’s break down the problem step by step:
Given: – Total Cost Price (C.P.): Rs. 1,000 – Cost of Fruits Sold at 10% Profit: Rs. 400 – Desired Overall Profit: 20%
Step 1: Calculate the Desired Total Selling Price
The desired overall profit is 20% of the total cost price. Therefore, the total selling price (S.P.) should be:
To achieve an overall 20% profit, the remaining fruits must be sold at a profit of approximately 26.67%.
#30. A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?
A. 50%
B. 80%
C. 75%
D. 66\( \frac{2}{3} \)
Answer: Option A Solution: To determine the percentage above the cost price at which the dealer listed his wares, let’s break down the problem step by step:
Given: – Cost Price (C.P.): Rs. 1 – Cash Discount Offered: 20% – Profit Made: 20% – Additional Offer:16 articles for the price of 12
Step 1: Calculate the Selling Price (S.P.)
The dealer makes a 20% profit on the cost price. Therefore, the selling price is:
The dealer listed his wares at 50% above the cost price.
#31. A man buys a chair and table for Rs. 6000. He sells the chair at a loss of 10% and the table at gain of 10%. He still gains Rs. 100 on the whole. Cost price of chair is:
A. Rs. 2500
B. Rs. 2850
C. Rs. 3050
D. Rs. 3500
Answer: Option A Solution: To determine the cost price of the chair, let’s break down the problem step by step:
Given: – Total Cost Price (C.P.): Rs. 6,000 – Loss on Chair: 10% – Gain on Table: 10% – Overall Gain: Rs. 100
Step 1: Define Variables Let: – C.P. of Chair: Rs. x – C.P. of Table: Rs. (6,000 – x)
Step 2: Calculate Selling Prices – Selling Price of Chair: \[ \text{S.P. of Chair} = x \times (1 – 0.10) = 0.90x \] -Selling Price of Table: \[ \text{S.P. of Table} = (6,000 – x) \times (1 + 0.10) = 1.10 \times (6,000 – x) \]
Step 3: Set Up the Equation for Overall Gain The total selling price is the sum of the selling prices of the chair and table. The overall gain is Rs. 100, so: \[ \text{Total S.P.} = \text{C.P.} + 100 \] \[ 0.90x + 1.10 \times (6,000 – x) = 6,000 + 100 \] Simplifying the equation: \[ 0.90x + 6,600 – 1.10x = 6,100 \] \[ -0.20x + 6,600 = 6,100 \] \[ -0.20x = -500 \] \[ x = \frac{-500}{-0.20} = 2,500 \]
Conclusion: The cost price of the chair is Rs. 2,500.
#32. By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:
A. Rs. 2600
B. Rs.2700
C. Rs. 2800
D. Rs. 3000
Answer: Option B Solution: To solve this, we first need to calculate the cost price (C.P.) of the bicycle.
So, the profit percentage based on the cost price is 33.33%.
#34. Two successive price increase of 10% and 10% of an article are equivalent to a single price increase of
A. 26\( \frac{2}{3} \)
B. 25%
C. 21%
D. 33\( \frac{1}{3} \)
Answer: Option C Solution: To calculate the effect of two successive price increases of 10% each, we use the following approach:
Let the original price of the article be \( P \).
1. First price increase: A 10% increase means the new price becomes: \[ P_1 = P \times 1.10 \]
2. Second price increase: The second 10% increase is applied to \( P_1 \), so the price after the second increase is: \[ P_2 = P_1 \times 1.10 = P \times 1.10 \times 1.10 = P \times (1.10)^2 \]
Now, calculate \( (1.10)^2 \):
\[ (1.10)^2 = 1.21 \]
Therefore, the overall effect of two successive 10% increases is equivalent to a single price increase of 21%.
#35. A stockiest wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit? (I. Sell sugar at 10% profit. II. Use 900 g of weight instead of 1 kg. III. Mix 10% impurities in sugar and selling sugar at cost price. IV. Increase the price by 5% and reduced weights by 5%.)
A. I or II
B. II
C. II, III and IV
D. Profits are same
E. None of these
Answer: Option B Solution: Let’s analyze each option in detail to see which one would maximize the stockist’s profit:
I. Sell sugar at 10% profit: – The stockist would sell sugar at 10% above the cost price. This is a straightforward way to make a profit. – The profit margin is 10%, but it’s a fixed profit, and the stockist’s profit would depend on how much sugar is sold.
II. Use 900 g of weight instead of 1 kg: – By selling 900 grams of sugar while claiming it to be 1 kilogram, the stockist is essentially reducing the quantity but still charging the full price for 1 kilogram. – This method could lead to profit because the stockist is selling less than what is being advertised. – The stockist could make a 10% profit in this case, as they are selling 900 grams for the price of 1 kilogram. This would effectively be a 10% increase in profit margin.
III. Mix 10% impurities in sugar and selling sugar at cost price: – Mixing impurities means the stockist is selling sugar mixed with lower-quality material but at the same price as pure sugar. – This could technically increase the profit because the stockist is using less pure sugar to sell at the same price. – However, this could harm the stockist’s reputation and lead to legal or ethical issues in the long term.
IV. Increase the price by 5% and reduce the weight by 5%: – Increasing the price by 5% and reducing the weight by 5% would lead to a higher price per unit of sugar while still giving less quantity to the customer. – This would increase the profit margin as both the price and the effective selling weight are altered to the stockist’s advantage.
Which Method Maximizes Profit?
– Option II (Use 900 g of weight instead of 1 kg) and Option IV (Increase the price by 5% and reduce the weight by 5%) are the two methods that could maximize profit. – Option II allows the stockist to sell less sugar for the same price, resulting in a 10% higher profit. – Option IV gives both a price increase and a reduction in quantity, increasing the profit margin.
Conclusion:Option IV (Increase the price by 5% and reduce the weight by 5%) would likely maximize the stockist’s profit, as it combines both a price increase and a reduction in quantity. However, Option II could also work effectively by selling less for the same price.
#36. A rickshaw dealer buys 30 rickshaws for Rs. 4725. Of these, 8 are four-seaters and the rest are two seaters. At what price must he sell the four-seaters so that if he sells the two-two seaters at \( \frac{2}{3} \)th of this price,he makes a profit 40% on his outlay?
A. Rs. 180
B. Rs. 292.5
C. Rs. 360
D. Rs. 450
E. None of these
Answer: Option B Solution: Let’s go step by step to solve the problem.
Step 1: Calculate the Cost Price (C.P.) of Each Rickshaw The dealer buys 30 rickshaws for Rs. 4725. So, the cost price per rickshaw is:
\[ \text{C.P. per rickshaw} = \frac{4725}{30} = 157.5 \]
Thus, the cost price of each rickshaw is Rs. 157.5.
Step 2: Identify the Cost Prices for Four-Seaters and Two-Seaters There are 8 four-seaters and 22 two-seaters. The total cost price for each type is:
Step 3: Calculate the Total Required Selling Price for a 40% Profit The dealer wants to make a 40% profit on his total outlay of Rs. 4725. The total selling price required to achieve this profit is:
Step 4: Let the Selling Price of a Four-Seater Be \( x \) Let the selling price of each four-seater be \( x \). The selling price of each two-seater is \( \frac{2}{3} \times x \), as given.
Step 5: Express the Total Selling Price The total selling price is the sum of the selling prices of all four-seaters and two-seaters. The total selling price is:
\[ \text{Total Selling Price} = 8 \times x + 22 \times \left( \frac{2}{3} \times x \right) \]
Final Answer: The dealer must sell each four-seater at Rs. 292.5 to make a 40% profit.
#37. A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres? (revenue per passenger is same)
A. 20%
B. 33.33%
C. 100%
D. 65.66%
E. Data inadequate
Answer: Option C Solution: Let’s break the problem into steps:
Step 1: Understand the First Scenario (3 Passengers, 20% Profit) – The driver carries 3 passengers and makes a profit of 20% per trip. – Let’s assume the cost of petrol used per trip is \( C_{\text{petrol}} \), and the revenue per passenger is \( R \).
The total revenue for 3 passengers would be:
\[ \text{Revenue} = 3 \times R \]
Since the profit is 20%, the cost price (C.P.) of the trip is calculated using the formula:
Now, the cost of petrol per trip is \( C_{\text{petrol}} \), and it is used in the total cost of the trip. Let’s say the petrol used per trip is \( x \) litres, and the price of petrol is Rs. 30 per litre:
\[ C_{\text{petrol}} = 30x \]
So the total cost price \( C.P. \) is the cost of petrol, which is \( 30x \).
Now, substituting the cost price into the equation:
\[ 3R = 1.20 \times 30x \]
\[ 3R = 36x \]
So, the revenue per passenger is:
\[ R = 12x \]
Step 2: Second Scenario (4 Passengers, Petrol Price Rs. 24) Now, let’s consider the scenario with 4 passengers and the price of petrol reduced to Rs. 24 per litre.
The revenue per passenger remains the same, so the total revenue for 4 passengers is:
Final Answer: The profit percentage for the same journey with 4 passengers and reduced petrol price is 100%.
#38. A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900 gram weight instead of a 1 kilogram weight. Find his percentage profit due to these maneuvers?
A. 8%
B. 12%
C. 20%
D. 16%
Answer: Option C Solution: Let’s break down the situation step by step:
Step 1: Understand the Dealer’s Maneuvers – The dealer marks up the price by 20%. – The dealer gives a 10% discount on the marked price. – The dealer uses a 900-gram weight instead of a 1-kg weight.
We need to find the overall profit percentage from these actions.
Step 2: Cost Price of Goods Let the cost price of the goods be Rs. \( C \) for 1 kg.
Step 3: Marked Price The dealer marks up the price by 20%, so the marked price of 1 kg is:
\[ \text{Marked Price} = C \times (1 + 0.20) = C \times 1.20 \]
Step 4: Selling Price After Discount The dealer gives a 10% discount on the marked price, so the selling price after the discount is:
Thus, the selling price of 1 kg (after the discount) is \( 1.08 \times C \).
Step 5: Quantity of Goods Sold The dealer uses a 900-gram weight instead of a 1-kg weight, so the customer actually receives only 900 grams for the price of 1 kg.
Step 6: Profit The dealer’s profit is the difference between the selling price and the cost price. The customer pays for 1 kg but receives only 900 grams, so the cost price of 900 grams is:
\[ \text{Cost Price of 900 grams} = C \times \frac{900}{1000} = 0.9C \]
The selling price of 900 grams is \( 1.08 \times C \). Thus, the profit is:
Final Answer: The dishonest dealer’s percentage profit due to these maneuvers is 20%.
#39. A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. He also uses a 900 gram weight instead of a 1 kilogram weight. Find his percentage profit due to these maneuvers?
A. 20%
B. 11%
C. 14%
D. 18%
E. None of these
Answer: Option A Solution: Let’s calculate the percentage profit made by the dishonest dealer based on the given information:
Step 1: Cost Price of the Goods Let the cost price of 1 kg of goods be \( C \).
Step 2: Marked Price The dealer marks up the price of the goods by 20%. So, the marked price for 1 kg of goods is:
\[ \text{Marked Price} = C \times (1 + 0.20) = C \times 1.20 \]
Step 3: Selling Price After Discount The dealer gives a 10% discount on the marked price. So, the selling price after the discount is:
Thus, the selling price for 1 kg (after the discount) is \( 1.08 \times C \).
Step 4: Quantity of Goods Sold The dealer uses a 900-gram weight instead of a 1-kg weight. So, for the price of 1 kg, the customer receives only 900 grams of goods. The cost price of 900 grams is:
\[ \text{Cost Price of 900 grams} = C \times \frac{900}{1000} = 0.9C \]
Step 5: Profit Made by the Dealer The selling price for 900 grams (after the discount) is \( 1.08 \times C \). The dealer’s cost price for 900 grams is \( 0.9 \times C \). So, the profit is:
Final Answer: The dishonest dealer’s percentage profit due to these maneuvers is 20%.
#40. The cost of setting up the type of a magazine is Rs. 1000. The cost of running the printing machine is Rs.120 per 100 copies. The cost of paper, ink and so on is 60 paise per copy. The magazines are sold at Rs. 2.75 each. 900 copies are printed, but only 784 copies are sold. What is the sum to be obtained from advertisements to give profit of 10% on the cost?
A. Rs. 730
B. Rs. 720
C. Rs. 726
D. Rs. 736
E. Rs. 750
Answer: Option C Solution: Let’s break down the problem and calculate the sum to be obtained from advertisements to give a 10% profit on the cost.
Step 1: Fixed and Variable Costs
1. Fixed Cost: The cost of setting up the type of the magazine is Rs. 1000.
2. Variable Costs: – Cost of running the printing machine: Rs. 120 per 100 copies. For 900 copies, the cost is: \[ \text{Printing cost} = \frac{120}{100} \times 900 = 1080 \]
– Cost of paper, ink, and so on: 60 paise (Rs. 0.60) per copy. For 900 copies, the cost is: \[ \text{Paper and ink cost} = 0.60 \times 900 = 540 \]
Step 2: Total Cost The total cost of producing 900 copies is the sum of the fixed cost and the variable costs:
Step 6: Amount to be Obtained from Advertisements The revenue from sales is Rs. 2156, and the total amount needed is Rs. 2882. The amount to be obtained from advertisements is the difference:
Final Answer: The sum to be obtained from advertisements to give a profit of 10% on the cost is Rs. 726.
#41. A tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage altogether?
A. 14.875%
B. 15.375%
C. 15.575%
D. 16.375%
E. 16.5%
Answer: Option B Solution: Let the cost price of the goods be \( C \) per unit.
Step 1: Determine the selling price
The selling price is 30% above the cost price, so:
\[ \text{Selling Price} = C + 0.30C = 1.30C \]
Step 2: Breakdown of stock sold
– Half of the stock is sold at the original selling price: Selling price for half the stock = \( 1.30C \).
– One-quarter of the stock is sold at a 15% discount: Discounted selling price = \( 1.30C \times (1 – 0.15) = 1.30C \times 0.85 = 1.105C \).
– The remaining one-quarter is sold at a 30% discount: Discounted selling price = \( 1.30C \times (1 – 0.30) = 1.30C \times 0.70 = 0.91C \).
Step 3: Calculate total revenue
Let’s assume the total stock is 1 unit for simplicity. The quantities sold and their respective selling prices are:
– Half of the stock: \( 0.5 \times 1.30C = 0.65C \). – One-quarter of the stock: \( 0.25 \times 1.105C = 0.27625C \). – One-quarter of the stock: \( 0.25 \times 0.91C = 0.2275C \).
#42. A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper?
A. 20%
B. 25%
C. 32%
D. 46.66%
E. 50%
Answer: Option A Solution: Let’s break this problem down step by step:
Step 1: Understand the Cost Price (C.P.) Let the cost price (C.P.) of 1 kg of goods for the dealer be \( C \) rupees.
Step 2: Markup and Discount
– The dealer marks up the price by 20%. The marked price (M.P.) is therefore:
\[ \text{Marked Price} = C + 0.20C = 1.20C \]
– The dealer gives a discount of 10% on the marked price. So, the selling price (S.P.) after the discount is:
– When the dealer buys 1 kg, he receives 1 kg but only pays for 900 grams. Therefore, his effective cost price for 1 kg is based on receiving more goods for less money. The effective cost price is:
#43. Ajay bought a motor cycle for Rs. 50,000. 2 years later he sold it to Vijay at 10% less of the cost price. Vijay spend 5% of the purchasing price on its maintenance. Later Vijay displayed the sale price of his motorcycle Rs. 50,000. Chetan wanted to purchase it at 15% discount but Vijay gave him two successive discounts of 10% and 5% instead of 15% in one time. What is the actual discount availed by Chetan?
A. 15%
B. 15.5%
C. 14.5 %
D. 16.5%
E. Cannot determined
Answer: Option C Solution: Let’s break down the problem step by step:
Step 1: Ajay’s Purchase and Sale to Vijay
– Ajay’s purchase price: Ajay bought the motorcycle for Rs. 50,000.
– Vijay’s purchase price: After 2 years, Ajay sold the motorcycle to Vijay at 10% less than the cost price.
Final Answer: The actual discount availed by Chetan is 14.5%.
#44. A trader sells goods to a customer at a profit of k% over the cost price, besides it he cheats his customer by giving 880 g only instead of 1 kg. Thus his overall profit percentage is 25%. Find the value of k?
A. 8.33%
B. 8.25%
C. 10%
D. 12.5%
Answer: Option C Solution: Let’s break this problem down step by step:
Step 1: Let the Cost Price (C.P.) of 1 kg be \( C \)
– The trader sells the goods at a profit of \( k\% \) over the cost price. Therefore, the selling price (S.P.) for 1 kg, with the profit included, is:
\[ \text{Selling Price} = C + \frac{k}{100} \times C = C \left( 1 + \frac{k}{100} \right) \]
Step 2: The Cheating Aspect
– The trader cheats the customer by giving only 880 grams instead of 1 kg, but he charges the full price for 1 kg. Thus, for every 1 kg the customer is supposed to receive, the trader actually gives only 880 grams.
The trader’s cost for 880 grams is:
\[ \text{Cost Price for 880 grams} = \frac{880}{1000} \times C = 0.88C \]
Step 3: Overall Profit Percentage
The trader’s selling price for 1 kg (i.e., 1000 grams) is \( C \left( 1 + \frac{k}{100} \right) \), but his cost for the 880 grams is \( 0.88C \).
\[ C \left( 0.12 + \frac{k}{100} \right) = 0.22C \]
Dividing both sides by \( C \) (assuming \( C \neq 0 \)):
\[ 0.12 + \frac{k}{100} = 0.22 \]
Step 5: Solve for \( k \)
Now, solve for \( k \):
\[ \frac{k}{100} = 0.22 – 0.12 = 0.10 \]
\[ k = 0.10 \times 100 = 10 \]
Final Answer: The value of \( k \) is 10.
#45. A retailer increase the selling price by 25% due to which his profit percentage increase from 20% to 25%. What is the percentage increase in cost price ?
A. 20%
B. 30%
C. 25%
D. 50%
Answer: Option A Solution: Let’s break the problem into manageable steps:
Step 1: Define the Variables
Let the initial cost price of the item be \( C \).
– The initial selling price (S.P.) is based on a profit of 20% over the cost price. So, the initial selling price is:
#47. The cost of setting up a magazine is Rs. 2800. The cost of paper and ink etc is Rs. 80 per 100 copies and printing cost is Rs. 160 per 100 copies. In last month 2000 copies were printed but only 1500 copies could be sold at Rs. 5 each. Total 25% profit on the sale price was realized. There is one more resource of income from magazine which is advertising. What sum of money obtained from the advertising in magazine?
A. Rs. 1750
B. Rs. 2350
C. Rs. 1150
D. Rs. 975
E. None of these
Answer: Option D Solution: Let’s break down the problem step by step to find the money obtained from advertising.
Step 1: Calculate the Total Costs
– Setting up cost: Rs. 2800 (fixed cost).
– Cost of paper and ink: Rs. 80 per 100 copies. Since 2000 copies were printed, the total cost for paper and ink is:
\[ \text{Cost of paper and ink} = \frac{2000}{100} \times 80 = 20 \times 80 = 1600 \]
– Printing cost: Rs. 160 per 100 copies. The total printing cost for 2000 copies is:
The problem states that a 25% profit on the sale price was realized. The total sale price from selling 1500 copies is Rs. 7500, and the profit is 25% of the sale price:
The total profit (Rs. 1875) is the sum of the profit from the sale and the advertising revenue. The total cost to produce 2000 copies was Rs. 7600, and the revenue from the sale of 1500 copies was Rs. 7500, so the advertising revenue must make up the difference between the total cost, the revenue from sales, and the total profit.
Final Answer: The sum of money obtained from advertising in the magazine is Rs. 975.
#48. A person bought a certain quantity of rice at the rate of Rs. 150/quintal. 10% of the rice was spoiled. At what rate(per quintal) should he sell the remaining rice to earn 20% profit.
A. Rs. 180
B. Rs. 200
C. Rs. 210
D. Rs. 220
Answer: Option B Solution: Let’s solve this problem step by step.
Step 1: Define the variables
– Let the total quantity of rice be \( x \) quintals. – The cost price of the rice is Rs. 150 per quintal, so the total cost price for \( x \) quintals is:
\[ \text{Total Cost Price} = 150 \times x \]
Step 2: Account for the spoiled rice
– 10% of the rice was spoiled, so the remaining rice is 90% of the total quantity. Therefore, the remaining rice is:
\[ \text{Remaining Rice} = 0.90 \times x \]
Step 3: Calculate the selling price needed to earn 20% profit
– The person wants to earn a 20% profit on the total cost price. So, the total selling price required to earn a 20% profit is:
\[ \text{Selling Price per Quintal} = \frac{180}{0.90} = 200 \]
Final Answer: The person should sell the remaining rice at Rs. 200 per quintal to earn a 20% profit.
#49. A trader sells two brands of petrol; one is Extra Premium and other one is speed. He mixes 12 litres Extra Premium with 3 litres of speed and by selling this mixture at the price of Extra Premium he gets the profit of 9.09. If the price of Extra Premium Rs. 48 per litre, then the price of Speed is:
A. Rs. 38 per litre
B. Rs. 42 per litre
C. Rs. 28 per litre
D. Rs. 18 per litre
E. None of These
Answer: Option C Solution: Let’s break the problem into steps to find the price of Speed.
Step 1: Define the variables
– Let the price of Speed per litre be \( x \) (this is what we need to find). – The price of Extra Premium is Rs. 48 per litre.
Step 2: Cost of the mixture
The trader mixes 12 litres of Extra Premium with 3 litres of Speed.
– The total cost of 12 litres of Extra Premium is:
\[ \text{Cost of Extra Premium} = 12 \times 48 = 576 \]
– The total cost of 3 litres of Speed is:
\[ \text{Cost of Speed} = 3 \times x \]
Thus, the total cost of the mixture is:
\[ \text{Total Cost of Mixture} = 576 + 3x \]
Step 3: Selling the mixture
The trader sells the mixture at the price of Extra Premium (Rs. 48 per litre). The total quantity of the mixture is:
Now, bring all terms involving \( x \) to one side and constants to the other side:
\[ 14400 – 5234.64 = 300x + 27.27x \]
\[ 9165.36 = 327.27x \]
Solve for \( x \):
\[ x = \frac{9165.36}{327.27} \approx 28 \]
Final Answer: The price of Speed is Rs. 28 per litre.
#50. Kamal bought a house, whose sale price was Rs. 8 lakh. He availed 20% discount as an early bird offer and then 10% discount due to cash payment. After that he spent 10% of the cost price in interior decoration and lawn of the house. At what price should he sell the house to earn a profit of 25%?
A. Rs. 9 lakh
B. Rs. 7.99 lakh
C. Rs. 7.92 lakh
D. Rs. 7 lakh
E. None of These
Answer: Option C Solution: Let’s solve the problem step by step:
Step 1: Calculate the price after discounts
The original sale price of the house is Rs. 8,00,000.
– First discount (20%): Kamal gets a 20% discount as an early bird offer. The price after the first discount is:
Step 2: Calculate the cost of interior decoration and lawn
Kamal spends 10% of the cost price (after discounts) on interior decoration and lawn. The cost after discounts is Rs. 5,76,000, so the cost of interior decoration and lawn is:
\[ \text{Cost of decoration and lawn} = 5,76,000 \times 0.10 = 57,600 \]
So, the total cost incurred by Kamal, including the price of the house and decoration, is:
