Comparing Quantities (Profit & Loss) worksheet - Free Printable
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Step-by-step solution for: Comparing Quantities (Profit & Loss) worksheet
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Step-by-step solution for: Comparing Quantities (Profit & Loss) worksheet
Let's solve each problem step by step.
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Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss percent.
Solution:
- Cost Price (CP) = Rs 1240
- Selling Price (SP) = Rs 1147
Loss = CP - SP = 1240 - 1147 = Rs 93
Loss Percent = \(\frac{\text{Loss}}{\text{CP}} \times 100\)
\[ \text{Loss Percent} = \frac{93}{1240} \times 100 = 7.5\% \]
Answer: Loss = Rs 93, Loss Percent = 7.5%
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A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the radio for Rs 300, determine his profit percent.
Solution:
- Cost Price (CP) = Purchase Price + Overhead Expenses = 225 + 15 = Rs 240
- Selling Price (SP) = Rs 300
Profit = SP - CP = 300 - 240 = Rs 60
Profit Percent = \(\frac{\text{Profit}}{\text{CP}} \times 100\)
\[ \text{Profit Percent} = \frac{60}{240} \times 100 = 25\% \]
Answer: Profit Percent = 25%
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A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent.
Solution:
- Cost Price (CP) = Purchase Price + Overhead Expenses = 1200 + 40 = Rs 1240
- Selling Price (SP) = Rs 1550
Profit = SP - CP = 1550 - 1240 = Rs 310
Profit Percent = \(\frac{\text{Profit}}{\text{CP}} \times 100\)
\[ \text{Profit Percent} = \frac{310}{1240} \times 100 = 25\% \]
Answer: Profit Percent = 25%
---
A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs 300, find his profit percent.
Solution:
- Cost Price (CP) = Purchase Price + Repair Costs = 225 + 15 = Rs 240
- Selling Price (SP) = Rs 300
Profit = SP - CP = 300 - 240 = Rs 60
Profit Percent = \(\frac{\text{Profit}}{\text{CP}} \times 100\)
\[ \text{Profit Percent} = \frac{60}{240} \times 100 = 25\% \]
Answer: Profit Percent = 25%
---
If the selling price of 10 pens is equal to the cost price of 14 pens, find the gain percent.
Solution:
Let the cost price of 1 pen be \( C \) and the selling price of 1 pen be \( S \).
- Selling price of 10 pens = Cost price of 14 pens
\[ 10S = 14C \]
\[ S = \frac{14C}{10} = 1.4C \]
Gain = Selling Price - Cost Price = \( S - C = 1.4C - C = 0.4C \)
Gain Percent = \(\frac{\text{Gain}}{\text{CP}} \times 100\)
\[ \text{Gain Percent} = \frac{0.4C}{C} \times 100 = 40\% \]
Answer: Gain Percent = 40%
---
If the selling price of 18 chairs is equal to the selling price of 16 chairs, find the gain or loss percent.
Solution:
Let the cost price of 1 chair be \( C \) and the selling price of 1 chair be \( S \).
- Selling price of 18 chairs = Selling price of 16 chairs
\[ 18S = 16C \]
\[ S = \frac{16C}{18} = \frac{8C}{9} \]
Since \( S < C \), there is a loss.
Loss = Cost Price - Selling Price = \( C - S = C - \frac{8C}{9} = \frac{C}{9} \)
Loss Percent = \(\frac{\text{Loss}}{\text{CP}} \times 100\)
\[ \text{Loss Percent} = \frac{\frac{C}{9}}{C} \times 100 = \frac{100}{9} \approx 11.11\% \]
Answer: Loss Percent = 11.11%
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By selling a book for Rs 258, a bookseller gains 20%. For how much should he sell it to gain 30%?
Solution:
- Let the cost price of the book be \( C \).
- Given that the bookseller gains 20% when selling for Rs 258:
\[ \text{Selling Price (SP)} = C + 0.2C = 1.2C \]
\[ 1.2C = 258 \]
\[ C = \frac{258}{1.2} = 215 \]
To find the selling price for a 30% gain:
\[ \text{New Selling Price} = C + 0.3C = 1.3C \]
\[ \text{New Selling Price} = 1.3 \times 215 = 279.5 \]
Answer: The bookseller should sell the book for Rs 279.50.
---
A defective briefcase costing Rs 800 is being sold at a loss of 8%. If the price is further reduced by 5%, find its selling price.
Solution:
- Original Cost Price (CP) = Rs 800
- First Reduction (8% loss):
\[ \text{Selling Price after 8% loss} = 800 - 0.08 \times 800 = 800 \times 0.92 = 736 \]
- Second Reduction (5% further reduction):
\[ \text{Final Selling Price} = 736 - 0.05 \times 736 = 736 \times 0.95 = 700.20 \]
Answer: Final Selling Price = Rs 700.20
---
By selling 90 ball pens for Rs 160, a person loses 20%. How many ball pens should be sold for Rs 96 so as to have a profit of 20%?
Solution:
- Cost Price (CP) of 90 ball pens:
Let the cost price of 90 ball pens be \( C \).
\[ \text{Selling Price (SP)} = C - 0.2C = 0.8C \]
\[ 0.8C = 160 \]
\[ C = \frac{160}{0.8} = 200 \]
So, the cost price of 90 ball pens is Rs 200. Therefore, the cost price of 1 ball pen is:
\[ \text{Cost Price of 1 ball pen} = \frac{200}{90} = \frac{20}{9} \]
- To achieve a 20% profit on selling some ball pens for Rs 96:
Let the number of ball pens sold be \( x \).
\[ \text{Selling Price (SP)} = 96 \]
\[ \text{Cost Price (CP)} = x \times \frac{20}{9} \]
For a 20% profit:
\[ \text{SP} = \text{CP} + 0.2 \times \text{CP} = 1.2 \times \text{CP} \]
\[ 96 = 1.2 \times \left( x \times \frac{20}{9} \right) \]
\[ 96 = x \times \frac{24}{9} \]
\[ 96 = x \times \frac{8}{3} \]
\[ x = \frac{96 \times 3}{8} = 36 \]
Answer: The person should sell 36 ball pens for Rs 96 to achieve a 20% profit.
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A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.
Solution:
- Let the original cost price of the article be \( C \).
- Case 1: Original Sale
\[ \text{Selling Price (SP)} = C + 0.25C = 1.25C \]
- Case 2: Hypothetical Sale
If the cost price was 20% less:
\[ \text{New Cost Price} = C - 0.2C = 0.8C \]
\[ \text{New Selling Price} = 1.25C - 36.75 \]
For a 30% profit:
\[ \text{New Selling Price} = 0.8C + 0.3 \times 0.8C = 1.04C \]
Equating the two expressions for the new selling price:
\[ 1.25C - 36.75 = 1.04C \]
\[ 1.25C - 1.04C = 36.75 \]
\[ 0.21C = 36.75 \]
\[ C = \frac{36.75}{0.21} = 175 \]
Answer: The cost price of the article is Rs 175.
---
1. Loss = Rs 93, Loss Percent = 7.5%
2. Profit Percent = 25%
3. Profit Percent = 25%
4. Profit Percent = 25%
5. Gain Percent = 40%
6. Loss Percent = 11.11%
7. Selling Price for 30% gain = Rs 279.50
8. Final Selling Price = Rs 700.20
9. Number of ball pens = 36
10. Cost Price = Rs 175
\[
\boxed{175}
\]
---
Problem 1:
Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss percent.
Solution:
- Cost Price (CP) = Rs 1240
- Selling Price (SP) = Rs 1147
Loss = CP - SP = 1240 - 1147 = Rs 93
Loss Percent = \(\frac{\text{Loss}}{\text{CP}} \times 100\)
\[ \text{Loss Percent} = \frac{93}{1240} \times 100 = 7.5\% \]
Answer: Loss = Rs 93, Loss Percent = 7.5%
---
Problem 2:
A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the radio for Rs 300, determine his profit percent.
Solution:
- Cost Price (CP) = Purchase Price + Overhead Expenses = 225 + 15 = Rs 240
- Selling Price (SP) = Rs 300
Profit = SP - CP = 300 - 240 = Rs 60
Profit Percent = \(\frac{\text{Profit}}{\text{CP}} \times 100\)
\[ \text{Profit Percent} = \frac{60}{240} \times 100 = 25\% \]
Answer: Profit Percent = 25%
---
Problem 3:
A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent.
Solution:
- Cost Price (CP) = Purchase Price + Overhead Expenses = 1200 + 40 = Rs 1240
- Selling Price (SP) = Rs 1550
Profit = SP - CP = 1550 - 1240 = Rs 310
Profit Percent = \(\frac{\text{Profit}}{\text{CP}} \times 100\)
\[ \text{Profit Percent} = \frac{310}{1240} \times 100 = 25\% \]
Answer: Profit Percent = 25%
---
Problem 4:
A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs 300, find his profit percent.
Solution:
- Cost Price (CP) = Purchase Price + Repair Costs = 225 + 15 = Rs 240
- Selling Price (SP) = Rs 300
Profit = SP - CP = 300 - 240 = Rs 60
Profit Percent = \(\frac{\text{Profit}}{\text{CP}} \times 100\)
\[ \text{Profit Percent} = \frac{60}{240} \times 100 = 25\% \]
Answer: Profit Percent = 25%
---
Problem 5:
If the selling price of 10 pens is equal to the cost price of 14 pens, find the gain percent.
Solution:
Let the cost price of 1 pen be \( C \) and the selling price of 1 pen be \( S \).
- Selling price of 10 pens = Cost price of 14 pens
\[ 10S = 14C \]
\[ S = \frac{14C}{10} = 1.4C \]
Gain = Selling Price - Cost Price = \( S - C = 1.4C - C = 0.4C \)
Gain Percent = \(\frac{\text{Gain}}{\text{CP}} \times 100\)
\[ \text{Gain Percent} = \frac{0.4C}{C} \times 100 = 40\% \]
Answer: Gain Percent = 40%
---
Problem 6:
If the selling price of 18 chairs is equal to the selling price of 16 chairs, find the gain or loss percent.
Solution:
Let the cost price of 1 chair be \( C \) and the selling price of 1 chair be \( S \).
- Selling price of 18 chairs = Selling price of 16 chairs
\[ 18S = 16C \]
\[ S = \frac{16C}{18} = \frac{8C}{9} \]
Since \( S < C \), there is a loss.
Loss = Cost Price - Selling Price = \( C - S = C - \frac{8C}{9} = \frac{C}{9} \)
Loss Percent = \(\frac{\text{Loss}}{\text{CP}} \times 100\)
\[ \text{Loss Percent} = \frac{\frac{C}{9}}{C} \times 100 = \frac{100}{9} \approx 11.11\% \]
Answer: Loss Percent = 11.11%
---
Problem 7:
By selling a book for Rs 258, a bookseller gains 20%. For how much should he sell it to gain 30%?
Solution:
- Let the cost price of the book be \( C \).
- Given that the bookseller gains 20% when selling for Rs 258:
\[ \text{Selling Price (SP)} = C + 0.2C = 1.2C \]
\[ 1.2C = 258 \]
\[ C = \frac{258}{1.2} = 215 \]
To find the selling price for a 30% gain:
\[ \text{New Selling Price} = C + 0.3C = 1.3C \]
\[ \text{New Selling Price} = 1.3 \times 215 = 279.5 \]
Answer: The bookseller should sell the book for Rs 279.50.
---
Problem 8:
A defective briefcase costing Rs 800 is being sold at a loss of 8%. If the price is further reduced by 5%, find its selling price.
Solution:
- Original Cost Price (CP) = Rs 800
- First Reduction (8% loss):
\[ \text{Selling Price after 8% loss} = 800 - 0.08 \times 800 = 800 \times 0.92 = 736 \]
- Second Reduction (5% further reduction):
\[ \text{Final Selling Price} = 736 - 0.05 \times 736 = 736 \times 0.95 = 700.20 \]
Answer: Final Selling Price = Rs 700.20
---
Problem 9:
By selling 90 ball pens for Rs 160, a person loses 20%. How many ball pens should be sold for Rs 96 so as to have a profit of 20%?
Solution:
- Cost Price (CP) of 90 ball pens:
Let the cost price of 90 ball pens be \( C \).
\[ \text{Selling Price (SP)} = C - 0.2C = 0.8C \]
\[ 0.8C = 160 \]
\[ C = \frac{160}{0.8} = 200 \]
So, the cost price of 90 ball pens is Rs 200. Therefore, the cost price of 1 ball pen is:
\[ \text{Cost Price of 1 ball pen} = \frac{200}{90} = \frac{20}{9} \]
- To achieve a 20% profit on selling some ball pens for Rs 96:
Let the number of ball pens sold be \( x \).
\[ \text{Selling Price (SP)} = 96 \]
\[ \text{Cost Price (CP)} = x \times \frac{20}{9} \]
For a 20% profit:
\[ \text{SP} = \text{CP} + 0.2 \times \text{CP} = 1.2 \times \text{CP} \]
\[ 96 = 1.2 \times \left( x \times \frac{20}{9} \right) \]
\[ 96 = x \times \frac{24}{9} \]
\[ 96 = x \times \frac{8}{3} \]
\[ x = \frac{96 \times 3}{8} = 36 \]
Answer: The person should sell 36 ball pens for Rs 96 to achieve a 20% profit.
---
Problem 10:
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.
Solution:
- Let the original cost price of the article be \( C \).
- Case 1: Original Sale
\[ \text{Selling Price (SP)} = C + 0.25C = 1.25C \]
- Case 2: Hypothetical Sale
If the cost price was 20% less:
\[ \text{New Cost Price} = C - 0.2C = 0.8C \]
\[ \text{New Selling Price} = 1.25C - 36.75 \]
For a 30% profit:
\[ \text{New Selling Price} = 0.8C + 0.3 \times 0.8C = 1.04C \]
Equating the two expressions for the new selling price:
\[ 1.25C - 36.75 = 1.04C \]
\[ 1.25C - 1.04C = 36.75 \]
\[ 0.21C = 36.75 \]
\[ C = \frac{36.75}{0.21} = 175 \]
Answer: The cost price of the article is Rs 175.
---
Final Answers:
1. Loss = Rs 93, Loss Percent = 7.5%
2. Profit Percent = 25%
3. Profit Percent = 25%
4. Profit Percent = 25%
5. Gain Percent = 40%
6. Loss Percent = 11.11%
7. Selling Price for 30% gain = Rs 279.50
8. Final Selling Price = Rs 700.20
9. Number of ball pens = 36
10. Cost Price = Rs 175
\[
\boxed{175}
\]
Parent Tip: Review the logic above to help your child master the concept of profit and loss worksheet.
