# Exercise : 6

^{2}⁄

_{7}?

(b) 14 : 56

(c) 15 : 56

(d) 16 : 72

(e) None of these

**Ans.a**

Let the ratio be x: (x + 40).Then,

\(\frac{x}{\left( x + 40 \right)} = \frac{2}{7}\) ⇒ 2x + 80 ⇒ x = 16.∴ Required ratio = 16 : 56.

(b) 18 years

(c) 15 years

(d) 9 years

(e) None of these

**Ans.c**

Total age of 3 boys = (25 × 3) years = 75 years. Ratio of their ages = 3 : 5 : 7.

Age of the youngest = (75 × ^{3}⁄_{15}) years = 15 years.

^{1''}⁄

_{2}× 1

^{7''}⁄

_{8}is to be enlarged so that the length will be 4”. How many inches will the enlarged breadth be?

^{1}⁄

_{2}

(b) 2

^{1}⁄

_{8}

(c) 3

(d) 3

^{3}⁄

_{8}

(e) None of these

**Ans.c**

Let enlarged breadth be x inches. Then,

^{5}⁄_{2} : 4 :: ^{15}⁄_{8} : x

⇒ ^{5}⁄_{2}x = 4 × ^{15}⁄_{8} ⇒ x = 3 inches.

^{1}⁄

_{6}of the capital for

^{1}⁄

_{6}of the time, B invests

^{1}⁄

_{3}of the capital for

^{1}⁄

_{3}of the time and C, the rest of the capital for whole time. Find A’s share of the total profit of 2,300.

(b) 200

(c) 300

(d) 400

(e) None of these

**Ans.a**

Remaining capital = 1 - (^{1}⁄_{6} + ^{1}⁄_{3}) = ^{1}⁄_{2}

Ratio of their profit

= ^{1}⁄_{6} × [^{1}⁄_{6} × 12] : ^{1}⁄_{3} × [^{1}⁄_{3} × 12] : ^{1}⁄_{2} × 12

= ^{1}⁄_{3} : ^{4}⁄_{3} : 6 = 1 : 4 : 18

∴ A's share = \(\frac{1}{1 + 4 + 18} \times 2300\) = 100

(b) 21,200

(c) 28,200

(d) 20,500

(e) None of these

**Ans.c**

Ratio of the capitals of A, B and C

= 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7

= 205000 : 212000 : 282000 = 205 : 212 : 282.

B’s share = (69900 × ^{212}⁄_{699}) = 21200;

(b) 4600

(c) 5400

(d) 4800

(e) None of these

**Ans.b**

The amount A gets for managing

= 12.5% of Rs. 8800 = 1100

Remaining profit = 8800 – 1100 = 7700

This is to be divided in the ratio 5 : 6.

Share of A = 5/11 of 7700 = 3500

⇒ Total share of A = 3500 + 1100 = 4600.

(b) 9 months

(c) 10 months

(d) 7 months

(e) None of these

**Ans.a**

Let B join after x months of the start of the business so that B’s money is invested for (12 – x) months.

∴ Profit ratio is 12 × 12500 : (12 – x) × 37500

or 12 : 3(12 – x)

Since profit is equally divided so

12 = 3(12 – x) or x = 8. Thus B joined after 8 months.

(b) 10 months after

(c) 7 months after

(d) 12 months after

(e) None of these

**Ans.c**

Let B join after ‘x’ month of the start of the business.

⇒ (45,000 × 12) : 54,000 × (12 – x) = 2 : 1

∴ (45,000 × 12) × 1 = 54,000 × (12 – x) × 2

⇒ x = 7

(b) 8 months

(c) 6 months

(d) 7 months

(e) None of these

**Ans.a**

Initially A’s investment = 3x and B’s investment = 4x

Let B remain in the business for ‘n’ months.

⇒ 3x × 10 : 4x × n = 5 : 6

∴ 3x × 10 × 6 = 4x × n × 5

⇒ n = 9

(b) 360

(c) 350

(d) 260

(e) None of these

**Ans.b**

In a year, for A, total amount as a remuneration

= 10 × 12 = 120

∴ Amount of A’s profit = 390 – 120 = 270

Ratio of investment = 3 : 4

Let total profit = x

Then, B’s profit = (x – 270)

∴ \(\frac{3}{3 + 4} \times x = 270\) ⇒ x = 630

∴ B’s profit = 630 – 270 = 360