Exercise : 6


1. What is the ratio whose terms differ by 40 and the measure of which is 27?
(a) 16 : 56
(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.

2. The average age of three boys is 25 years and their ages are in the proportion 3 : 5 : 7. The age of the youngest boy is:
(a) 21 years
(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 × 315) years = 15 years.

3. A photograph measuring 21''2 × 17''8 is to be enlarged so that the length will be 4”. How many inches will the enlarged breadth be?
(a) 112
(b) 218
(c) 3
(d) 338
(e) None of these
Ans.c

Let enlarged breadth be x inches. Then,

52 : 4 :: 158 : x

52x = 4 × 158 ⇒ x = 3 inches.

4. In a partnership, A invests 16 of the capital for 16 of the time, B invests 13 of the capital for 13 of the time and C, the rest of the capital for whole time. Find A’s share of the total profit of 2,300.
(a) 100
(b) 200
(c) 300
(d) 400
(e) None of these
Ans.a

Remaining capital = 1 - (16 + 13) = 12

Ratio of their profit

= 16 × [16 × 12] : 13 × [13 × 12] : 12 × 12

= 13 : 43 : 6 = 1 : 4 : 18

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

5. A, B and C start a business each investing 20,000. After 5 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 69,900 was recorded. Find the share of B.
(a) 20,000
(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 × 212699) = 21200;

6. A is a working partner and B is a sleeping partner in a business. A puts in 50,000 and B 60,000. A gets 12.5% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of A in profit of 8800.
(a) 3500
(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.

7. A began business with 12500 and is joined afterwards by B with 37500. When did B join, if the profits at the end of the year are divided equally?
(a) 8 months
(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.

8. A began business with 45,000 and was later joined by B with 54,000. When did B join if the profit at the end of the year were divided in the ratio 2 : 1?
(a) 5 months after
(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

9. A and B enter into partnership with capitals in the ratio 3 : 4. At the end of 10 months A withdraws,and the profits now are divided in the ratio of 5 : 6. Find how long B remained in the business?
(a) 9 months
(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

10. A and B invest 3,000 and 4,000 in a business. A receives 10 per month out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investments. If in a year ‘A’ totally receives 390, what does B receive?
(a) 375
(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