Percentages

12
 Question 1
John earns 33.33% more than Peter. By what percentage is Peter's earning less than that of John's?
 A 22 % B 25 % C 26 % D 23 %
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Question 1 Explanation:
Let John's income be j and Peter's income be p. Then, j = p + p × 33.33% = p + p × 100⁄3 % = p + p × 1/3 = 4p/3 ⇒ p = 3j/4 = (4 - 1)j/4 = j - j/4 = j - j × 1/4 = j - j × 100⁄4 % = j - j × 25%. Therefore, Peter's earning is less than John's earning by 25%.
 Question 2
Mary's salary is reduced by 10%. By what percentage must her new salary be increased in order to gain her old salary?
 A 137⁄9 % B 194⁄9 % C 100/9 % D 110⁄9 %
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Question 2 Explanation:
Let her old salary be Rs 100. Then, her new salary = 100 - 10 = Rs 90. So, to gain her old salary, her new salary must be increased by Rs 10. Therefore, the required percentage = (10⁄90) × 100% = 100/9 %.
 Question 3
The price of sugar is decreased by 10%. As a consequence, monthly sales is increased by 30%. Find out the percentage increase in monthly revenue.
 A 17 % B 19 % C 18 % D None of these
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Question 3 Explanation:
Let the price of sugar be Rs 100 and monthly sales be 100 units. Then, total revenue = 100 × 100 = Rs 10000. And, new revenue = 90 × 130 = Rs 11700. Increase in revenue = 11700 - 10000 = Rs 1700. Hence, percentage increase in revenue = (1700/10000) × 100% = 17%.
 Question 4
Jack consumes 75% of his salary. Later his salary is increased by 20% and he increases his expenditures by 10%. Find the percentage increase in his savings.
 A 51% B 60% C 50% D 55%
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Question 4 Explanation:
Let Jack's original salary be Rs 100. Then, his expenditure = Rs 75, his savings = Rs 25. Now, his new salary = Rs 120. So, new expenditure = (110/100) × 75 = Rs 165/2, new savings = 120 - 165/2 = Rs 75/2. Increase in savings = 75/2 - 25 = Rs 25/2. Therefore, percentage increase in savings = (25/2)/25 × 100% = 50%.
 Question 5
Mary buys an item at Rs 25 in a sale and saves Rs 5. Find out the percentage of her savings.
 A 40/3 % B 55/3 % C 50/3 % D None of these
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Question 5 Explanation:
Original Price of the item = 25 + 5 = Rs 30. Hence, the required percentage = (5/30) × 100% = 50/3 %.
 Question 6
Barack spends Rs 6650 to buy some goods and gets a rebate of 6% on it. After this, he pays a sales tax of 10%. What is his total expenditure?
 A Rs 6870.10 B Rs 6876.10 C Rs 6865.10 D Rs 6776.10
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Question 6 Explanation:
Rebate received by Barack = 6% of Rs 6650 = 6/100 × 6650 = 3/5 × 665 = Rs 399. Sales Tax paid by Barack = 10% of Rs (6650-399) = 10% of Rs 6251 = Rs 625.10. Therefore, Barack's total expenditure = Rs (6251 + 625.10) = Rs 6876.10.
 Question 7
Felix spends 66.66% of his salary and saves Rs 1200 every month. Calculate his monthly expenditure in Rupees.
 A Rs 2402 B Rs 2400 C Rs 2401 D Rs 2405
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Question 7 Explanation:
Let Felix's monthly salary be Rs x. Then, (100 - 66.66)% of x = Rs 1200 ⇒ 33.33 % of x = Rs 1200 ⇒ x/3 = Rs 1200 ⇒ x = Rs 3600. Therefore, his monthly expenditure = 3600 - 1200 = Rs 2400.
 Question 8
Jack and Robert appeared in an examination. Robert scored 9 marks less than Jack. Jack's score was 56% of the sum of their scores added together. Calculate their individual scores.
 A 22 and 33 B 41 and 35 C 40 and 35 D 42 and 33
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Question 8 Explanation:
Let Robert's score be x. Then, Jack's score = x+9. Now, x+9 = 56% of [(x+9) + x] ⇒ x+9 = 14/25 × (2x + 9) ⇒ 25 × (x+9) = 14 × (2x+9) ⇒ 25x + 225 = 28x + 126 ⇒ 3x = 99 ⇒ x = 33. Therefore, Robert scored 33 marks and Jack scored 42 marks.
 Question 9
Ram spends 20% of is salary on food, 15 % of remaining on cloths, and 400 on entertainment. If his salary is 10000, how much he spends on food?
 A 2000 B 3000 C 1500 D 2500
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Question 9 Explanation:
10000*20/100 = 2000
 Question 10
Ram spends 20% of is salary on food, 15 % of remaining on cloths, and 400 on entertainment. If his salary is 10000, how much he spends on cloths?
 A 1100 B 1200 C 1500 D 1000
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Question 10 Explanation:
[10000-(10000*20/100)]*15/100 = 1200
There are 16 questions to complete.
12

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