# Exercise 4

1. Rajesh solved 80 per cent of the questions in an examination correctly. If out of 41 questions solved by Rajesh 37 questions are correct and of the remaining questions out of 8 questions 5 questions have been solved by Rajesh correctly then find the total number of questions asked in the examination.
(a) 75
(b) 65
(c) 60
(d) Cannot be determined
(e) None of these

#### View Ans & Explanation

Ans.b

Suppose there are 8x questions a part from the 41 questions.

Then, $\frac{37 + 5x}{41 + 8x} = 80\% = \frac{4}{5}$

⇒ 185 + 25x = 164 + 32x ⇒ 7x= 21 ⇒ x = 3

∴ Total no.of questions = 41 + 8x = 65

2. 10% of the inhabitants of a village having died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
(a) 5000
(b) 6000
(c) 7000
(d) 8000
(e) None of these

#### View Ans & Explanation

Ans.b

Let the total number of original inhabitants be x. Then,

(100 – 25)% of (100 –10)% of x = 4050

$\left(\frac{75}{100} \times \frac{90}{100} \times x \right)$ = 4050 ⇒ 2740x = 4050

⇒ x = $\frac{4050 \times 40}{27} = 6000.$

∴ Number of original inhabitants = 6000.

3. Chunilal invests 65% in machinery 20% in raw material ands till has 1,305 cash with him. Find his total investment.
(a) 6,500
(b) 7,225
(c) 8,500
(d) 7,395
(e) None of these

#### View Ans & Explanation

Ans.d

Let he had originally ₹ x.

Then 65% of x + 20 % of x + 1305 = x

0.65x + 0.2x + 1305 = x

⇒ 0.15 x = 1305 ⇒ x = ₹8700

∴ His total investment = 65% of 8700 + 20% of 8700

= 85% of 700 = ₹ 7395

4. When the price of a pressure cooker was increased by 15%, the sale of pressure cookers decreased by 15%. What was the net effect on the sales?
(a) 15% decrease
(b) no effect
(c) 2.25% increase
(d) 2.25% decrease
(e) None of these

#### View Ans & Explanation

Ans.d

Net effect on sale = $- \frac{\left(common \; \% \; change \right)^{2}}{100}$

= $- \frac{\left(15 \right)^{2}}{100}$ = 2.25% decrease

5. When the price of a radio was reduced by 20%, its sale increased by 80%. What was the net effect on the sale?
(a) 44% increase
(b) 44% decrease
(c) 66% increase
(d) 75% increase
(e) None of these

#### View Ans & Explanation

Ans.a

Let the original price be x and sale be of y units.

Then, the revenue collected initially = x × y

Now, new price = 0.8x, new sale = 1.8y

Then, new revenue collected = 1.44xy

% increase in revenue = $\frac{0.44xy}{xy} \times 100$

= 44% increase

6. When the price of sugar was increased by 32%, a family reduced its consumption in such a way that the expenditure on sugar was only 10% more than before. If 30 kg were consumed per month before, find the new monthly consumption.
(a) 20 kg
(b) 25 kg
(c) 30 kg
(d) 35 kg
(e) None of these

#### View Ans & Explanation

Ans.b

Since, expenditure = price × consumption

∴ 110% of 30 = 132100 × new consumption

110100 × 30 = 132100 × new consumption

⇒ New consumption = 25 kg

7. If 10 % of an electricity bill is deducted, 45 is still to be paid. How much was the bill?
(a) 50
(b) 60
(c) 55
(d) 70
(e) None of these

#### View Ans & Explanation

Ans.a

Let the bill be x. Then

90% of x = 45

⇒ x = $\frac{45 \times 100}{90}$ = ₹ 50

8. The ratio of salary of a worker in July to that in June was 212 : 214, by what % the salary of July more than salary of June. Also find by what %, salary of June was less than that of July.
(a) 1119% and 10%
(b) 10% and 1119%
(c) Both 10%
(d) Both 1119%
(e) None of these

#### View Ans & Explanation

Ans.a

Let the salary of July be ₹ 52 x

and the salary of June be ₹ 94 x

Required percentages

= $\frac{\frac{5}{2}x - \frac{9}{4}x}{\frac{9}{4}x} \times 100 \;\; and \;\; \frac{\frac{5}{2}x - \frac{9}{4}x}{\frac{5}{2}x} \times 100$

= 1009% and 10010% = 1119% and 10%

9. 405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?
(a) 7
(b) 9
(c) 18
(d) 45
(e) None of these

#### View Ans & Explanation

Ans.b

Let the total number of children be x.

Then, x × (20 % of x) = 405

15 x2 = 405 ⇔ x2 = 2025 ⇔ x = 45

∴ Number of sweets received by each child

= 20% of 45 = 9

10. There is an increase of 30% in the production of milk chocolates in Amul Dairy in one month. If now it is 9,100 milk chocolates per month, what was it one month ago?
(a) 10,000 chocolates
(b) 9000 chocolates
(c) 8000 chocolates
(d) 7000 chocolates
(e) None of these

#### View Ans & Explanation

Ans.d

Let one month ago, production be x chocolates.

Then, 130 % of x = 9100

⇒ x = $\frac{9100 \times 100}{130} = 7000 \; chocolates$

11. In a college election between two rivals, a candidate who got 40% of the total votes polled, was defeated by his rival by 160 votes. The total number of votes polled was
(a) 900
(b) 800
(c) 700
(d) 600
(e) None of these

#### View Ans & Explanation

Ans.b

Let total number of votes polled be x.

Then, votes polled by other candidate

= (100 – 40)% of x = 60% of x

Now 60% of x – 40% of x = 160

20x100 = 160 ⇒ x = 800 votes

12. A scooter costs 25,000 when it is brand new. At the end of each year, its value is only 80% of what it was at the beginning of the year. What is the value of the scooter at the end of 3 years?
(a) 10,000
(b) 12,500
(c) 12,800
(d) 12,000
(e) None of these

#### View Ans & Explanation

Ans.c

After first year, the value of the scooter = ₹ 20,000

After second year, the value of scooter = ₹ 16,000

After third year, the value of scooter = ₹ 12,800

13. A number is increased by 11% and then reduced by 10%. After these operations, the number :
(a) does not change
(b) decreases by 1%
(c) increases by 1%
(d) increases by 0.1%
(e) None of these

#### View Ans & Explanation

Ans.b

Let the original number be 100.

Then, the new number = 100 × 1.1 × 0.9 = 99

i.e. the number decreases by 1%.