Exercise : 7


1. A started a business with 4500 and another person B joined after some period with 3000. Determine this period after B joined the business if the profit at the end of the year is divided in the ratio 2 : 1
(a) After 3 months
(b) After 4 months
(c) After 6 months
(d) After 212 months
(e) None of these
Ans.a

Let B joined after x months.

Then, 4500 × 12 : 3000 (12 – x) = 2 : 1

Ratio of their investments

\(\frac{4500 \times 12}{3000\left(12 - x \right)} = \frac{2}{1}\) ⇒ x = 3

2. A and B entered into a partnership with capitals in the ratio of 4 : 5. After 3 months, A withdrew 14 of his capital and B withdrew 15 of his capital. The gain at the end of 10 months was 760. Find the profit of B
(a) 450
(b) 430
(c) 410
(d) 340
(e) None of these
Ans.b

Let A’s capital = 4x and B’s capital = 5x

∴ Ratio of profit

= 4x \times 3 + \frac{3}{4}\left(4x \right) \times 7 : 5x \times 3 + \frac{4}{5} \left(5x \right) \times 7\(

= 33 : 43

? Profit of B = \)\frac{43}{33 + 43} \times 760\( = 430

3. A and B rent a pasture for 10 months; A puts in 80 cows for 7 months. How many can B put in for the remaining 3 months,if he pays half as much again as A?
(a) 120
(b) 180
(c) 200
(d) 280
(e) None of these
Ans.d

Let B puts = x cows

then amount paid by B = 3?2 amount paid by A.

? \)\frac{80 \times 7}{x \times 3} = \frac{amount \; paid \; by \; A}{\frac{3}{2} \times amount \; paid \; by \; A}\(

? x = \)\frac{80 \times 7 \times 3}{3 \times 2}\( = 280 cows

4. In a partnership between X and Y, X?s capital is 2?5 of total and is invested for 2?5 year. If his share of the profit is 4?7 of the total, for how long is Y?s capital in the business?
(a) 1 year
(b) 18 years
(c) 13 years
(d) 14 years
(e) None of these
Ans.c

? X?s capital = 2?5 of total

? Y?s capital = 1- 2?5 = 3?5 of total

Let Y invested capital for t years.

? Ratio of profit = 2?5 2?3 : 3?5 t

= 4?15 : 3t?5 ...(i)

Share of Y?s profit = 1 - 4?7 = 3?7 of the total

Actual ratio of profit = 4 : 3

? By (i), \)\frac{\frac{4}{15}}{\frac{3t}{5}}\( = 4?3 ? t =1?3 year.

5. X and Y put in 3,000 and 4,000 respectively into a business. X reinvests into the business his share of the first year?s profit of 2,100 whereas Y does not reinvest. In what ratio should they share the second year?s profit?
(a) 39 : 40
(b) 3 : 4
(c) 3 : 7
(d) 40 : 79
(e) None of these
Ans.a

For first year, ratio of profit = 3 : 4

X?s profit of first year = 3?7 2100 = 900

Now, for second year,Now, for second year,

ratio of profit = 3000 12 + 900 12 : 4000 12

= 46800 : 48000 = 39 :40

6. Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water?
(a) 2 : 3
(b) 3 : 2
(c) 1 : 3
(d) 2 : 1
(e) None of these
Ans.b

By the rule of alligation, we have

ap1

? Required ratio = 6?4 = 3 : 2

7. Six litres of a 20% solution of alcohol in water are mixed with 4 litres of a 60% solution of alcohol in water. The % alcoholic strength of the mixture is
(a) 80
(b) 40
(c) 36
(d) 48
(e) None of these
Ans.c

% alcoholic strength in mixture = \)\frac{6 \times 20 + 4 \times 60}{6 + 4}\( = 36 %

8. A merchant lent out `1,000 in two parts, one at 8% and the other at 10% interest. The yearly average comes out to be 9.2%. Find the amount lent in two parts.
(a) 400, 600
(b) 500, 500
(c) 300, 700
(d) cannot be determined
(e) None of these
Ans.a

\)\frac{Quantity \; lent \; at \; 8\%}{Quantity \; lent \; at \; 10\%} = \frac{10 - 9.2}{9.2 - 8} = \frac{0.8}{1.2} = \frac{2}{3}\(

? Quantity of money lent at 8%

= \)\frac{2}{2 + 3} \times 1000\( = 400

and quantity of money lent at 10%

= \)\frac{3}{2 + 3} \times 1000\( = 600

9. One litre of water was mixed to 3 litres of sugar solution containing 4% of sugar. What is the percentage of sugar in the solution?
(a) 3
(b) 4
(c) 6
(d) Insufficient data
(e) None of these
Ans.a

New % of sugar in (3 + 1) litre solution

= \)\frac{0.04 \times 3}{\left(3 + 1 \right)} = 0.03 = 3 \%$$ = 600

10. How much water must be added to 60 litres of milk at 112 litres for 20 so as to have a mixture worth 1023 a litre?
(a) 10 litres
(b) 12 litres
(c) 15 litres
(d) 18 litres
(e) None of these
Ans.c

C.P. of 1 litre of milk = (20 × 23) = 403

5

∴ Ratio of water and milk = 83 : 323 = 8 : 32 = 1 : 4

∴ Quantity of water to be added to 60 litres of milk

= (14 × 60) litres = 15 litres.