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71. Jhon, Mona and Gordon, three US based business partners, jointly invested in a business project to supply nuclear fuel to India. As per their share in the investment, Gordon will receive $\frac{2}{3}$ of the profits whereas Jhon and Mona divided the remainder equally. It is estimated that the income of Jhon will increase by $ 60 million when the rate of profit rises from 4% to 7%. What is Mona's capital ?

A. $ 2000 million

B. $ 3000 million

C. $ 5000 million

D. $ 8000 million

Discuss

Solution:

Fraction of profit received by each one of Jhon and Mona

\begin{aligned} = \frac{(1 - \frac{2}{3})}{2} \\ = \frac{1}{6} \end{aligned}

Ratio of capitals of Jhon, Mona and Gordon = Ratio of their profits

\begin{aligned} \frac{1}{6} : \frac{1}{6} : \frac{2}{3} = 1 : 1 : 4 \\ Let the total capital be Rs . x \\ Then, \\ \frac{1}{6} of (7 % of x - 4 % of x) \\ = $ 60 million \\ \Rightarrow 3 % of x = $ 3 60 million \\ \Rightarrow x = $ (\frac{360 \times 100}{3}) million \\ \Rightarrow x = $ 12000 million \\ ∴ Mona's capital \\ = (\frac{1}{6} \times $ 12000 million) \\ = $ 200 0 million \end{aligned}

72. Anu is a working partner and Bimla is a sleeping partner in a business. Anu puts Rs. 5000 and Bimla putes in Rs. 6000. Anu receives 12.5% of the profit for managing the business and the rest is divided in proportion to their capitals. What does each get put of a profit of Rs. 880 ?

A. Rs. 400, Rs. 480

B. Rs. 450, Rs. 430

C. Rs. 460, Rs. 420

D. Rs. 470, Rs. 410

Discuss

Solution:

\begin{aligned} = Anu : Bimla \\ = 5000 : 6000 \\ = 5 : 6 \end{aligned}

Anu's share for managing business

\begin{aligned} = 12.5 % of  Rs . 880 \\ = Rs . 110 \\ Net profit \\ = Rs . (880 - 110) \\ = Rs . 770 \\ Anu's share \\ = Rs . (770 \times \frac{5}{11}) \\ = Rs . 350 \\ Anu's total share \\ = Rs . (110 + 350) \\ = Rs . 460 \\ Bimla's share \\ = Rs . (770 \times \frac{6}{11}) \\ = Rs . 420 \end{aligned}

73. The ratio of investments of two partners X and Y is 11 : 12 and the ratio of their profit is 2 : 3. If X invested the money for 8 months, then the time for which Y invested the money is ?

A. 8 months

B. 9 months

C. 10 months

D. 11 months

Discuss

Solution:

Let capital of X be Rs. 11x and Y's capital be Rs. 12x
and let time for which Y invested capital is T₂ months
by using formula,

\begin{aligned} \Leftrightarrow \frac{C_{1} \times T_{1}}{C_{2} \times T_{2}} = \frac{P_{1}}{P_{2}} \\ \Leftrightarrow \frac{11 x \times 8}{12 x \times T_{2}} = \frac{2}{3} \\ \Leftrightarrow T_{2} = 11 months \end{aligned}

Hence the time for which Y invested his capital is 11 months

74. A and B enter into partnership. At the end of 9 months B withdraws but A's capitals is used for one month more. If they receive profit in the ratio of 5 : 6, then the ratio of their capital is ?

A. 3 : 4

B. 4 : 3

C. 5 : 6

D. 6 : 5

Discuss

Solution:

Let A's capital = Rs. x
Let B's capital = Rs. y
Now, according to the question,

	A	B
Capital →	x	y
Time (in month) →	(9 + 1) = 10	9
Ratio of profit →	5	6

\begin{aligned} We know, \\ \frac{10 \times x}{x \times y} = \frac{5}{6} \\ \Leftrightarrow \frac{x}{y} = \frac{3}{4} \end{aligned}

Hence the required ratio of capital of A and B is = 3 : 4

75. Two partners invested Rs. 125000 and Rs. 85000 respectively in a business. They distribute 60% of the profit equally and decide to distribute the remaining 40% as the interest on their capitals. If one partner received Rs. 3000 more than the other, the total profits is ?

A. Rs. 42250

B. Rs. 39375

C. Rs. 38840

D. Rs. 36575

Discuss

Solution:

\begin{aligned} Let the total profit be Rs . x \\ Then, 60 % of the profit \\ = Rs . (\frac{60}{100} \times x) \\ = Rs . \frac{3 x}{5} \end{aligned}

From this part of the profit each gets =

Rs . \frac{3 x}{10}

\begin{aligned} 40 % of total profit \\ = Rs . (\frac{40}{100} \times x) \\ = Rs . \frac{2 x}{5} \end{aligned}

Now, this amount of Rs.

\frac{2 x}{5}

has been divided in the ratio of capitals, which is 125000 : 85000 or 25 : 17 as interests
∴ Interest on first capital

\begin{aligned} = Rs . (\frac{2 x}{5} \times \frac{25}{42}) \\ =  Rs . \frac{5 x}{21} \end{aligned}

Interest on second capital

\begin{aligned} = Rs . (\frac{2 x}{5} \times \frac{17}{42}) \\ =  Rs . \frac{17 x}{105} \end{aligned}

Total money received by first partner

\begin{aligned} = Rs . (\frac{3 x}{10} + \frac{5 x}{21}) \\ =  Rs . \frac{113 x}{210} \end{aligned}

Total money received by second partner

\begin{aligned} = Rs . (\frac{3 x}{10} + \frac{17 x}{105}) \\ =  Rs . \frac{97 x}{210} \\ ∴ \frac{113 x}{210} - \frac{97 x}{210} = 3000 \\ \Rightarrow x = 39375 \\ Hence, \\ Total profit Rs . 39375 \end{aligned}

76. Nonad, Vikas and and Manav enter into a partnership. Ninad invest some amount at the beginning. Vikas invest double the amount after 6 months and Manav invests thrice the amount invested by Ninad after 8 months. They earn a profit of Rs. 45000 at the end of the year. What is Manav's share in the profit ?

A. Rs. 9000

B. Rs. 12000

C. Rs. 15000

D. Rs. 25000

Discuss

Solution:

\begin{aligned} Let Ninad's investment be Rs . x \\ Then, ratio of capitals \\ = (x \times 12) : (2 x \times 6) : (3 x \times 4) \\ = 12 x : 12 x : 12 x \\ = 1 : 1 : 1 \\ ∴ Manav's share \\ = Rs . (45000 \times \frac{1}{3}) \\ = Rs .15000 \end{aligned}

77. Four milkmen rented a pasture. A grazed 15 cows for 4 months, B grazed 12 cows for 2 months, C grazed 18 cows for 6 months and D grazed 16 cows for 5 months. If A's share of rent is Rs. 1020, what is C's share of rent ?

A. Rs. 916

B. Rs. 1360

C. Rs. 1836

D. Cannot be determined

Discuss

Solution:

\begin{aligned} = A : B : C : D \\ = 15 \times 4 : 12 \times 2 : 18 \times 6 : 16 \times 5 \\ = 60 : 24 : 108 : 80 \\ = 15 : 6 : 27 : 20 \\ Let the total rent be Rs . x \\ Then, \\ A's share = Rs . (\frac{15 x}{68}) \\ ∴ \frac{15 x}{68} = 1020 \\ \Rightarrow x = (\frac{1020 \times 68}{15}) \\ \Rightarrow x = 4624 \\ Hence, C's share \\ = Rs . (4624 \times \frac{27}{68}) \\ = Rs . 1836 \end{aligned}

78. A, B and C are three partners in a business. The profit share of A is $\frac{3}{16}$ of the total profit and B's share is $\frac{1}{4}$ of the total profit. If C receives Rs. 243, then the amount received by B will be ?

A. Rs. 90

B. Rs. 96

C. Rs. 108

D. Rs. 120

Discuss

Solution:

\begin{aligned} Let total profit = 16 units \\ According to the question, \\ Profit share of A \\ = \frac{3}{16} \times 16 units \\ = 3 units \\ profit share of B \\ = \frac{1}{4} \times 16 = 4 units \\ then profit share of C \\ = [16 - (4 + 3)] = 9 units \\ But profit of C = Rs . 243 (given) \\ 9 units = Rs . 243 \\ 1 unit = Rs . 27 \\ Profit share of B \\ = 4 units \\ = 27 \times 4 \\ = Rs . 108 \end{aligned}

79. A is a active partner and B is a inactive partner in business. A puts in Rs. 5000 and B puts in Rs. 6000. A received 15% of the profit for managing the business and the rest is divided in proportion to their capitals. The amounts received by A out of the profit of Rs. 880 in all is ?

A. Rs. 132

B. Rs. 340

C. Rs. 472

D. Rs. 492

Discuss

Solution:

Total profit = Rs. 880
Since A gets 15% of total profit for management
∴ Remaining profit

\begin{aligned} = 880 - \frac{880 \times 15}{100} \\ = Rs . 748 \end{aligned}

	A		B
Amount	5000		6000
Ratio of Capital	5	:	6

The remaining profit is being divided in the ratio of their capital
A's share of profit

\begin{aligned} = \frac{748}{(5 + 6)} \times 5 \\ = Rs . 340 \end{aligned}

Total profit received by A
= 340 + 132
= Rs. 472

80. A, B and C are partners in a business. Their shares are in the proportion of $\frac{1}{3} : \frac{1}{4} : \frac{1}{5}$ . A withdraws half of his capital after 15 months and after another 15 months, a profit of Rs. 4340 is divided. The share of C is ?

A. Rs. 1240

B. Rs. 1245

C. Rs. 1360

D. Rs. 1550

Discuss

Solution:

Ratio of initial investments

\begin{aligned} = \frac{1}{3} : \frac{1}{4} : \frac{1}{5} \\ = 20 : 15 : 12 \end{aligned}

Let their initial investments be 20x, 15x and 12x respectively
= A : B : C
= (20x × 15 + 10x × 15) : (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4

\begin{aligned} ∴ C's share \\ = Rs . (4340 \times \frac{4}{14}) \\ = Rs .1240 \end{aligned}

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