# Percentages

Question 1 |

John earns 33.33% more than Peter. By what percentage is Peter's earning less than that of John's?

22 % | |

25 % | |

26 % | |

23 % |

**Percentages**

**Discuss it**

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?

137⁄9 % | |

194⁄9 % | |

100/9 % | |

110⁄9 % |

**Percentages**

**Discuss it**

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.

17 % | |

19 % | |

18 % | |

None of these |

**Percentages**

**Discuss it**

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.

51% | |

60% | |

50% | |

55% |

**Percentages**

**Discuss it**

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.

40/3 % | |

55/3 % | |

50/3 % | |

None of these |

**Percentages**

**Discuss it**

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?

Rs 6870.10 | |

Rs 6876.10 | |

Rs 6865.10 | |

Rs 6776.10 |

**Percentages**

**Discuss it**

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.

Rs 2402 | |

Rs 2400 | |

Rs 2401 | |

Rs 2405 |

**Percentages**

**Discuss it**

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.

22 and 33 | |

41 and 35 | |

40 and 35 | |

42 and 33 |

**Percentages**

**Discuss it**

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?

2000 | |

3000 | |

1500 | |

2500 |

**Percentages**

**Discuss it**

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?

1100 | |

1200 | |

1500 | |

1000 |

**Percentages**

**Discuss it**

Question 10 Explanation:

[10000-(10000*20/100)]*15/100 = 1200

There are 16 questions to complete.