# Exercise 3

(b) 20,000

(c) 12,000

(d) Data inadequate

(e) None of these

**Ans.a**

N = R + 30% of R = 1.3 RR

= V – 20% of V = 80% of V = 0.8 V

∴ N = 1.3 × 0.8V = 1.04 V

Now, N – V = 1.04 V – V = 0.04 V = ₹ 800(given)

∴ V = ₹ 20000

∴ R = 0.8 × 20000 = ₹ 16000

(b) 5 : 4

(c) 2 : 3

(d) Data inadequate

(e) None of these

**Ans.a**

Let the population of males = x; then the population of females = 9000 – x

Now, 5% of x + 8% of (9000 – x)

= (9600 – 9000 ) = 600

or 0.05x + 720 – 0.08x = 600

or 720 – 600 = 0.08x – 0.05x

or, 120 = 0.03x

x = 4000

Reqd ratio of population of males and females

\(\frac{4000}{9000 - 4000} = \frac{4000}{5000} = 4 : 5\)(b) 900 ml

(c) 1900 ml

(d) 1800 ml

(e) None of these

**Ans.a**

In 1 lit mixture quantity of unleaded petrol = 100 ml

Let x ml leaded petrol be added, then

5% of (1000 + x) = 100 ml

or, 5 (1000 + x) = 100 × 100

⇒ x = ^{5000}⁄_{5} = 1000 ml

(b) 14

(c) 17

(d) Data inadequate

(e) None of these

**Ans.b**

Let the number of boys= x

then x + ^{7x}⁄_{10} = 85 or x = 50

No. of girls = 85 – 50 = 35

(b) 5% loss

(c) 8% loss

(d) Cannot be determined

(e) None of these

**Ans.c**

Net effect = + 15 – 20 – \(\frac{15 \times 20}{100} = -8\%\)

–ve sign indicates loss.

^{1}⁄

_{8}of

^{2}⁄

_{3}of

^{4}⁄

_{5}of a number is 12 then 30 per cent of the number will be

(b) 64

(c) 54

(d) 42

(e) None of these

**Ans.c**

Let the number be x.

and ^{1}⁄_{8} of ^{2}⁄_{3} of ^{4}⁄_{5} × x = 12

∴ ^{3x}⁄_{10} = 54

(b) 5.6

(c) 3.5

(d) 4.5

(e) None of these

**Ans.b**

Cost price of 20 dozen toys = 20 × 375 = 7,500

Selling price of 20 dozen toys = 20 × 33 × 12 = 7,920

Profit percentage = \(\frac{7920 - 7500}{7500} \times 100 = 5.6\%\)

(b) 30

(c) 25

(d) 20

(e) None of these

**Ans.a**

Let the truth spoken by A and B be p_{l} and p_{2}

respectively, i.e., p_{l} = ^{3}⁄_{4} and p_{2} = ^{4}⁄_{5}

They will contradict each other only when one speaks truth and the other is lying.

i.e., ^{3}⁄_{4} × ^{1}⁄_{5} + ^{4}⁄_{5} × ^{1}⁄_{4} = ^{3}⁄_{20} + ^{4}⁄_{20} = ^{7}⁄_{20} = ^{35}⁄_{100} i.e, 35%

(b) 12,000

(c) 16,000

(d) 20,000

(e) None of these

**Ans.c**

Food items = 40%

Clothes + conveyance = ^{1}⁄_{2} of 60% = 30%

^{1}⁄_{3} of 30% = ^{19,200}⁄_{12} ⇒ 10% = 1600

∴ 100% = ₹ 16,000

(b) 2 : 3

(c) 2 : 5

(d) Data inadequate

(e) None of these

**Ans.b**

30% of I + II = II × ^{120}⁄_{100}

or, ^{3}⁄_{10}I = ^{2}⁄_{10}II ⇒ I : II = 2 : 3.