# Exercise : 3

(b) 3 : 10 : 10

(c) 4 : 8 : 5

(d) 32 : 35 : 25

(e) None of these

**Ans.a**

Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 8x respectively.

When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes

3x × 120% : 5x × 140% :

8x × 125% = 36 : 70 : 100

= 18 : 35 : 50

(b) 32,500

(c) 38,281

(d) 52,500

(e) None of these

**Ans.e**

Ratio of Abhishek and Sudin for one month

= (50,000 × 36) + (30,000 × 24) : (70,000 × 24)

= (18,00,000 + 7,20,000) : 16,80,000 = 3 : 2

Hence share of Sudin in the profit earned from the business.

= \(\frac{87,500}{\left(3 + 2 \right)}\times 2\) = 35,000

(b) 17.5%

(c) 19%

(d) 21%

(e) None of these

**Ans.c**

Let the weights of Ram and Shyam be 4x and 5x. Now,according to question,

\(\frac{4x \times 110}{100} + Shyam?s \; new \; wt\) = 82.8........ (i)and 4x + 5x = \(\frac{9x + 115}{100}\) = 82.8........ (ii)

From (ii), x = 8

Putting in (i),

we get Shyam’s new wt = (82.8 – 35.2) = 47.6

% increase in Shyam’s wt = \(\left(\frac{47.6 - 40}{40} \times 100 \right)\) = 19%

(b) 3 : 4

(c) 2 : 3

(d) Data inadequate

(e) None of these

**Ans.c**

Let the numbers be y and x respectively

x + 50% of y = ^{4x}⁄_{3} or, ^{y}⁄_{2} = ^{4x}⁄_{3} - x

or, ^{y}⁄_{2} = ^{x}⁄_{3}

or, ^{y}⁄_{x} = ^{2}⁄_{3}

(b) 14

(c) 17

(d) Data inadequate

(e) None of these

**Ans.b**

Nisha Shilpa

7 8

4 9 10

Present age of Nisha = \(\frac{4 \times \left(10 - 9\right)}{9 \times 8 - 10 \times 7} \times 7\)

= 14 years

^{1}⁄

_{3}per cent of the second number. What is the ratio between the first and the second number?

(b) 7 : 4

(c) 7 : 3

(d) Data inadequate

(e) None of these

**Ans.c**

Let the first and second numbers be x and y respectively.

Then, x + y = ^{10}⁄_{3}y

or, x = ^{7}⁄_{3}y

∴ x : y = 7 : 3

(b) 20 years

(c) 24 years

(d) Data inadequate

(e) None of these

**Ans.e**

^{P}⁄_{Q} = ^{5}⁄_{8} or P = ^{5Q}⁄_{8} .....(i)

or, 3P + 12 = 2Q + 8 or, 2Q – 3P = 4... (ii)

Putting value of P from eq. (i),

2Q – 3 × ^{5}⁄_{8}Q = 4 ⇒ Q = 32

(b) 27.50

(c) 28.50

(d) 30.00

(e) 29.00

**Ans.a**

CP = 25 × 16.50 + 35 × 24.50 = 1270

SP = 1270 × ^{125}⁄_{100} = 1587.50

Price per kg = ^{1587.50}⁄_{60} ≈ 26.50

(b) 200 gms

(c) 800 gms

(d) 1.8 kg

(e) None of these

**Ans.a**

In 1 kg mixture quantity of iron = 200 gm

Let x gm sand should be added, then

10% of (1000 + x) = 200

\ x = 1000 gm = 1 kg

(b) 48 years

(c) 56 years

(d) Data inadequate

(e) None of these

**Ans.d**

^{P}⁄_{Q} = ^{5}⁄_{7}

or, Q = ^{7}⁄_{5}P

**Case I :** Q – (P + 6) = 2

or, Q = P + 8

∴ ^{7}⁄_{5}P = P + 8

or, 7P = 5P + 40

∴ P = ^{40}⁄_{2} = 20 and Q = ^{7}⁄_{5} × 20 = 28

P + Q = 20 + 28 = 48

**Case II :** (P + 6) – Q = 2

or, P + 6 – ^{7}⁄_{5}P = 2

or, P = –10 and Q = 14

∴ P + Q = 10 + 14 = 24 years