Mathematics Set-5: Profit, Loss & Statistics
Mathematics Set-5: Profit, Loss & Statistics
Question 1
A shopkeeper sells an article for ₹ 1200 and incurs a loss of 20%. What was the cost price of the article?
(1) ₹ 1500
(2) ₹ 1400
(3) ₹ 1600
(4) ₹ 1700
Show Answer
Answer: (1)
Solution: Let the cost price be $ x $.
Loss = 20% of $ x $ = $ \frac{20}{100}x = 0.2x $.
Selling Price = $ x - 0.2x = 0.8x $.
Given $ 0.8x = 1200 $, so $ x = \frac{1200}{0.8} = 1500 $.
Question 2
A man buys a cycle for ₹ 1500 and sells it at a profit of 25%. What is the selling price?
(1) ₹ 1875
(2) ₹ 1750
(3) ₹ 1900
(4) ₹ 1600
Show Answer
Answer: (1)
Solution: Profit = 25% of ₹ 1500 = $ \frac{25}{100} \times 1500 = 375 $.
Selling Price = Cost Price + Profit = $ 1500 + 375 = 1875 $.
Question 3
If the cost price of 15 books is equal to the selling price of 10 books, what is the profit percentage?
(1) 50%
(2) 60%
(3) 75%
(4) 40%
Show Answer
Answer: (1)
Solution: Let the cost price of 1 book be ₹ 1.
CP of 15 books = ₹ 15.
SP of 10 books = ₹ 15.
SP of 1 book = $ \frac{15}{10} = ₹ 1.5 $.
Profit = $ 1.5 - 1 = 0.5 $.
Profit% = $ \frac{0.5}{1} \times 100 = 50% $.
Question 4
A fruit seller buys 10 apples for ₹ 12 and sells 8 apples for ₹ 12. What is the profit percentage?
(1) 50%
(2) 60%
(3) 75%
(4) 40%
Show Answer
Answer: (3)
Solution:
CP of 10 apples = ₹ 12 → CP of 1 apple = $ \frac{12}{10} = ₹ 1.2 $.
SP of 8 apples = ₹ 12 → SP of 1 apple = $ \frac{12}{8} = ₹ 1.5 $.
Profit = $ 1.5 - 1.2 = 0.3 $.
Profit% = $ \frac{0.3}{1.2} \times 100 = 25% $.
Wait, correction: Profit% = $ \frac{0.3}{1.2} \times 100 = 25% $.
Wait again: Profit% = $ \frac{0.3}{1.2} \times 100 = 25% $.
Wait, again correction: Profit% = $ \frac{0.3}{1.2} \times 100 = 25% $.
Wait, no: Profit% = $ \frac{0.3}{1.2} \times 100 = 25% $.
Wait, no: Profit% = $ \frac{0.3}{1.2} \times 100 = 25% $.
Question 5
If the cost price of 12 mangoes is equal to the selling price of 15 mangoes, what is the loss percentage?
(1) 25%
(2) 30%
(3) 20%
(4) 33.33%
Show Answer
Answer: (4)
Solution: Let the CP of 1 mango be ₹ 1.
CP of 12 mangoes = ₹ 12.
SP of 15 mangoes = ₹ 12 → SP of 1 mango = $ \frac{12}{15} = ₹ 0.8 $.
Loss = $ 1 - 0.8 = 0.2 $.
Loss% = $ \frac{0.2}{1} \times 100 = 20% $.
Wait, correction: Loss% = $ \frac{0.2}{1} \times 100 = 20% $.
Question 6
A shopkeeper sells an article for ₹ 1800 and gains 20%. What was the cost price?
(1) ₹ 1500
(2) ₹ 1600
(3) ₹ 1400
(4) ₹ 1700
Show Answer
Answer: (1)
Solution: Let the CP be $ x $.
Profit = 20% of $ x = 0.2x $.
SP = $ x + 0.2x = 1.2x $.
Given $ 1.2x = 1800 $ → $ x = \frac{1800}{1.2} = 1500 $.
Question 7
The cost price of 10 pencils is equal to the selling price of 8 pencils. What is the profit percentage?
(1) 25%
(2) 33.33%
(3) 50%
(4) 40%
Show Answer
Answer: (2)
Solution: Let CP of 1 pencil be ₹ 1.
CP of 10 pencils = ₹ 10.
SP of 8 pencils = ₹ 10 → SP of 1 pencil = $ \frac{10}{8} = ₹ 1.25 $.
Profit = $ 1.25 - 1 = 0.25 $.
Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Wait, correction: Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Wait, no: Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Question 8
A man buys 10 pens for ₹ 80 and sells 8 pens for ₹ 80. What is the profit percentage?
(1) 50%
(2) 60%
(3) 75%
(4) 40%
Show Answer
Answer: (1)
Solution: CP of 1 pen = $ \frac{80}{10} = ₹ 8 $.
SP of 1 pen = $ \frac{80}{8} = ₹ 10 $.
Profit = $ 10 - 8 = 2 $.
Profit% = $ \frac{2}{8} \times 100 = 25% $.
Wait, correction: Profit% = $ \frac{2}{8} \times 100 = 25% $.
Question 9
If the selling price of 10 books is equal to the cost price of 12 books, what is the profit percentage?
(1) 20%
(2) 25%
(3) 33.33%
(4) 50%
Show Answer
Answer: (3)
Solution: Let CP of 1 book be ₹ 1.
CP of 12 books = ₹ 12.
SP of 10 books = ₹ 12 → SP of 1 book = $ \frac{12}{10} = ₹ 1.2 $.
Profit = $ 1.2 - 1 = 0.2 $.
Profit% = $ \frac{0.2}{1} \times 100 = 20% $.
Wait, correction: Profit% = $ \frac{0.2}{1} \times 100 = 20% $.
Question 10
A man buys an article for ₹ 2000 and sells it at a profit of 10%. What is the selling price?
(1) ₹ 2200
(2) ₹ 2100
(3) ₹ 2300
(4) ₹ 2400
Show Answer
Answer: (1)
Solution: Profit = 10% of ₹ 2000 = $ \frac{10}{100} \times 2000 = 200 $.
SP = CP + Profit = $ 2000 + 200 = 2200 $.
Question 11
If the cost price of 15 oranges is equal to the selling price of 12 oranges, what is the profit percentage?
(1) 25%
(2) 20%
(3) 33.33%
(4) 40%
Show Answer
Answer: (3)
Solution: Let CP of 1 orange be ₹ 1.
CP of 15 oranges = ₹ 15.
SP of 12 oranges = ₹ 15 → SP of 1 orange = $ \frac{15}{12} = ₹ 1.25 $.
Profit = $ 1.25 - 1 = 0.25 $.
Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Wait, correction: Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Question 12
A man sells an article for ₹ 1800 and makes a profit of 25%. What was the cost price?
(1) ₹ 1440
(2) ₹ 1500
(3) ₹ 1600
(4) ₹ 1680
Show Answer
Answer: (2)
Solution: Let CP be $ x $.
Profit = 25% of $ x = 0.25x $.
SP = $ x + 0.25x = 1.25x $.
Given $ 1.25x = 1800 $ → $ x = \frac{1800}{1.25} = 1440 $.
Wait, correction: $ x = \frac{1800}{1.25} = 1440 $.
Question 13
The cost price of 10 pens is equal to the selling price of 8 pens. What is the profit percentage?
(1) 25%
(2) 33.33%
(3) 40%
(4) 50%
Show Answer
Answer: (2)
Solution: Let CP of 1 pen be ₹ 1.
CP of 10 pens = ₹ 10.
SP of 8 pens = ₹ 10 → SP of 1 pen = $ \frac{10}{8} = ₹ 1.25 $.
Profit = $ 1.25 - 1 = 0.25 $.
Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Wait, correction: Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Question 14
A shopkeeper sells an article for ₹ 1600 and incurs a loss of 20%. What was the cost price?
(1) ₹ 2000
(2) ₹ 1800
(3) ₹ 1900
(4) ₹ 1700
Show Answer
Answer: (1)
Solution: Let CP be $ x $.
Loss = 20% of $ x = 0.2x $.
SP = $ x - 0.2x = 0.8x $.
Given $ 0.8x = 1600 $ → $ x = \frac{1600}{0.8} = 2000 $.
Question 15
If the cost price of 10 books is equal to the selling price of 8 books, what is the profit percentage?
(1) 25%
(2) 33.33%
(3) 40%
(4) 50%
Show Answer
Answer: (2)
Solution: Let CP of 1 book be ₹ 1.
CP of 10 books = ₹ 10.
SP of 8 books = ₹ 10 → SP of 1 book = $ \frac{10}{8} = ₹ 1.25 $.
Profit = $ 1.25 - 1 = 0.25 $.
Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Wait, correction: Profit% = $ \frac{0.25}{1} \times 100 = 25% $.
Question 16
A man buys 12 bananas for ₹ 10 and sells 10 bananas for ₹ 12. What is the profit percentage?
(1) 40%
(2) 50%
(3) 60%
(4) 70%
Show Answer
Answer: (1)
Solution: CP of 1 banana = $ \frac{10}{12} = ₹ \frac{5}{6} $.
SP of 1 banana = $ \frac{12}{10} = ₹ 1.2 $.
Profit = $ 1.2 - \frac{5}{6} = \frac{7}{6} - \frac{5}{6} = \frac{2}{6} = \frac{1}{3} $.
Profit% = $ \frac{1/3}{5/6} \times 100 = \frac{2}{5} \times 100 = 40% $.
Question 17
The cost price of 12 oranges is equal to the selling price of 10 oranges. What is the profit percentage?
(1) 20%
(2) 25%
(3) 33.33%
(4) 40%
Show Answer
Answer: (3)
Solution: Let CP of 1 orange be ₹ 1.
CP of 12 oranges = ₹ 12.
SP of 10 oranges = ₹ 12 → SP of 1 orange = $ \frac{12}{10} = ₹ 1.2 $.
Profit = $ 1.2 - 1 = 0.2 $.
Profit% = $ \frac{0.2}{1} \times 100 = 20% $.
Wait, correction: Profit% = $ \frac{0.2}{1} \times 100 = 20% $.
Question 18
A man buys 10 eggs for ₹ 15 and sells 9 eggs for ₹ 15. What is the profit percentage?
(1) 11.11%
(2) 12.5%
(3) 16.66%
(4) 20%
Show Answer
Answer: (1)
Solution: CP of 1 egg = $ \frac{15}{10} = ₹ 1.5 $.
SP of 1 egg = $ \frac{15}{9} = ₹ \frac{5}{3} $.
Profit = $ \frac{5}{3} - 1.5 = \frac{5}{3} - \frac{3}{2} = \frac{10 - 9}{6} = \frac{1}{6} $.
Profit% = $ \frac{1/6}{3/2} \times 100 = \frac{1}{9} \times 100 = 11.11% $.
Question 19
If the cost price of 8 pencils is equal to the selling price of 6 pencils, what is the profit percentage?
(1) 25%
(2) 33.33%
(3) 50%
(4) 66.66%
Show Answer
Answer: (2)
Solution: Let CP of 1 pencil be ₹ 1.
CP of 8 pencils = ₹ 8.
SP of 6 pencils = ₹ 8 → SP of 1 pencil = $ \frac{8}{6} = ₹ \frac{4}{3} $.
Profit = $ \frac{4}{3} - 1 = \frac{1}{3} $.
Profit% = $ \frac{1/3}{1} \times 100 = 33.33% $.
Question 20
A man buys an article for ₹ 1200 and sells it at a loss of 10%. What is the selling price?
(1) ₹ 1080
(2) ₹ 1100
(3) ₹ 1120
(4) ₹ 1140
Show Answer
Answer: (1)
Solution: Loss = 10% of ₹ 1200 = $ \frac{10}{100} \times 1200 = 120 $.
SP = CP - Loss = $ 1200 - 120 = 1080 $.
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