# Exercise 4

(b) 65

(c) 60

(d) Cannot be determined

(e) None of these

**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

(b) 6000

(c) 7000

(d) 8000

(e) None of these

**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 ⇒ ^{27}⁄_{40}x = 4050

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

∴ Number of original inhabitants = 6000.

(b) 7,225

(c) 8,500

(d) 7,395

(e) None of these

**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

(b) no effect

(c) 2.25% increase

(d) 2.25% decrease

(e) None of these

**Ans.d**

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

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

(b) 44% decrease

(c) 66% increase

(d) 75% increase

(e) None of these

**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

(b) 25 kg

(c) 30 kg

(d) 35 kg

(e) None of these

**Ans.b**

Since, expenditure = price × consumption

∴ 110% of 30 = ^{132}⁄_{100} × new consumption

⇒ ^{110}⁄_{100} × 30 = ^{132}⁄_{100} × new consumption

⇒ New consumption = 25 kg

(b) 60

(c) 55

(d) 70

(e) None of these

**Ans.a**

Let the bill be x. Then

90% of x = 45

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

^{1}⁄

_{2}: 2

^{1}⁄

_{4}, by what % the salary of July more than salary of June. Also find by what %, salary of June was less than that of July.

^{1}⁄

_{9}% and 10%

(b) 10% and 11

^{1}⁄

_{9}%

(c) Both 10%

(d) Both 11

^{1}⁄

_{9}%

(e) None of these

**Ans.a**

Let the salary of July be ₹ ^{5}⁄_{2} x

and the salary of June be ₹ ^{9}⁄_{4} x

Required percentages

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

= ^{100}⁄_{9}% and ^{100}⁄_{10}% = 11^{1}⁄_{9}% and 10%

(b) 9

(c) 18

(d) 45

(e) None of these

**Ans.b**

Let the total number of children be x.

Then, x × (20 % of x) = 405

⇔ ^{1}⁄_{5} x^{2} = 405 ⇔ x^{2} = 2025 ⇔ x = 45

∴ Number of sweets received by each child

= 20% of 45 = 9

(b) 9000 chocolates

(c) 8000 chocolates

(d) 7000 chocolates

(e) None of these

**Ans.d**

Let one month ago, production be x chocolates.

Then, 130 % of x = 9100

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

(b) 800

(c) 700

(d) 600

(e) None of these

**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

⇒ ^{20x}⁄_{100} = 160 ⇒ x = 800 votes

(b) 12,500

(c) 12,800

(d) 12,000

(e) None of these

**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

(b) decreases by 1%

(c) increases by 1%

(d) increases by 0.1%

(e) None of these

**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%.