Partnership - Aptitude MCQ Questions and Solutions with Explanations

Fraction of profit received by each one of Jhon and Mona
$$\eqalign{ & = \frac{{\left( {1 - \frac{2}{3}} \right)}}{2} \cr & = \frac{1}{6} \cr} $$
Ratio of capitals of Jhon, Mona and Gordon = Ratio of their profits
$$\eqalign{ & \frac{1}{6}:\frac{1}{6}:\frac{2}{3} = 1:1:4 \cr & {\text{Let the total capital be Rs}}{\text{.}}x \cr & {\text{Then,}} \cr & \frac{1}{6}{\text{of }}\left( {7\% {\text{ of }}x - 4\% {\text{ of }}x} \right) \cr & = \$ {\text{ 60 million}} \cr & \Rightarrow 3\% \,{\text{of }}x = \$ {\text{ }}3{\text{60 million}} \cr & \Rightarrow x = \$ \left( {\frac{{360 \times 100}}{3}} \right){\text{million}} \cr & \Rightarrow x = \$ {\text{ 12000 million }} \cr & \therefore {\text{ Mona's capital }} \cr & {\text{ = }}\left( {\frac{1}{6} \times \$ {\text{12000 million }}} \right) \cr & = \$ \,200{\text{0 million }} \cr} $$

$$\eqalign{ & = {\text{Anu}}:{\text{Bimla}} \cr & = 5000:6000 \cr & = 5:6{\text{ }} \cr} $$
Anu's share for managing business
$$\eqalign{ & = 12.5\% {\text{ of Rs}}{\text{.}}\,880 \cr & = {\text{Rs}}{\text{.}}\,110 \cr & {\text{Net profit}} \cr & = {\text{Rs}}{\text{.}}\left( {880 - 110} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{770}} \cr & {\text{Anu's share}} \cr & = {\text{Rs}}{\text{.}}\left( {770 \times \frac{5}{{11}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{350}} \cr & {\text{Anu's total share}} \cr & = {\text{Rs}}{\text{.}}\left( {110 + 350} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{460}} \cr & {\text{Bimla's share}} \cr & = {\text{Rs}}{\text{.}}\left( {770 \times \frac{6}{{11}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{420}} \cr} $$

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,
$$\eqalign{ & \Leftrightarrow \frac{{{{\text{C}}_1} \times {{\text{T}}_1}}}{{{{\text{C}}_2} \times {{\text{T}}_2}}} = \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} \cr & \Leftrightarrow \frac{{11x \times 8}}{{12x \times {{\text{T}}_2}}} = \frac{2}{3} \cr & \Leftrightarrow {{\text{T}}_2} = 11{\text{ months}} \cr} $$
Hence the time for which Y invested his capital is 11 months

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

$$\eqalign{ & {\text{We know,}} \cr & \frac{{10 \times x}}{{x \times y}} = \frac{5}{6} \cr & \Leftrightarrow \frac{x}{y} = \frac{3}{4} \cr} $$
Hence the required ratio of capital of A and B is = 3 : 4

$$\eqalign{ & {\text{Let the total profit be Rs}}{\text{. }}x \cr & {\text{Then, }}60\% {\text{ of the profit}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{60}}{{100}} \times x} \right) \cr & = {\text{Rs}}{\text{.}}\,\frac{{3x}}{5} \cr} $$
From this part of the profit each gets = $${\text{Rs}}{\text{.}}\,\frac{{3x}}{{10}}$$
$$\eqalign{ & 40\% {\text{ of total profit }} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{40}}{{100}} \times x} \right) \cr & = {\text{Rs}}{\text{.}}\,\frac{{2x}}{5} \cr} $$
Now, this amount of Rs. $$\frac{2x}{5}$$ has been divided in the ratio of capitals, which is 125000 : 85000 or 25 : 17 as interests
∴ Interest on first capital
$$\eqalign{ & = {\text{ Rs}}{\text{.}}\left( {\frac{{2x}}{5} \times \frac{{25}}{{42}}} \right) \cr & {\text{ = Rs}}{\text{.}}\,\frac{{5x}}{{21}} \cr} $$
Interest on second capital
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{2x}}{5} \times \frac{{17}}{{42}}} \right) \cr & {\text{ = Rs}}{\text{.}}\,\frac{{17x}}{{105}} \cr} $$
Total money received by first partner
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{3x}}{{10}} + \frac{{5x}}{{21}}} \right) \cr & {\text{ = Rs}}{\text{.}}\,\frac{{113x}}{{210}}{\text{ }} \cr} $$
Total money received by second partner
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{3x}}{{10}} + \frac{{17x}}{{105}}} \right) \cr & {\text{ = Rs}}{\text{.}}\,\frac{{97x}}{{210}} \cr & \therefore \frac{{113x}}{{210}} - \frac{{97x}}{{210}} = 3000 \cr & \Rightarrow x = 39375{\text{ }} \cr & {\text{Hence,}} \cr & {\text{Total profit Rs}}{\text{. 39375}} \cr} $$

$$\eqalign{ & {\text{Let Ninad's investment be Rs}}{\text{.}}x \cr & {\text{Then, ratio of capitals}} \cr & = \left( {x \times 12} \right):\left( {2x \times 6} \right):\left( {3x \times 4} \right) \cr & = 12x:12x:12x \cr & = 1:1:1 \cr & \therefore {\text{Manav's share}} \cr & = {\text{Rs}}{\text{.}}\left( {45000 \times \frac{1}{3}} \right) \cr & = {\text{Rs}}{\text{.15000}} \cr} $$

$$\eqalign{ & = {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & = 15 \times 4:12 \times 2:18 \times 6:16 \times 5 \cr & = 60:24:108:80 \cr & = 15:6:27:20 \cr & {\text{Let the total rent be Rs}}{\text{.}}x \cr & {\text{Then,}} \cr & {\text{A's share}} = {\text{Rs}}{\text{.}}\left( {\frac{{15x}}{{68}}} \right) \cr & \therefore \,\frac{{15x}}{{68}} = 1020 \cr & \Rightarrow x = \left( {\frac{{1020 \times 68}}{{15}}} \right) \cr & \Rightarrow x = 4624 \cr & {\text{Hence, C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {4624 \times \frac{{27}}{{68}}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{1836}} \cr} $$

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

Total profit = Rs. 880
Since A gets 15% of total profit for management
∴ Remaining profit
$$\eqalign{ & = 880 - \frac{{880 \times 15}}{{100}} \cr & = {\text{Rs}}.\,748 \cr} $$

	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
$$\eqalign{ & = \frac{{748}}{{\left( {5 + 6} \right)}} \times 5 \cr & = {\text{Rs}}.\,340 \cr} $$
Total profit received by A
= 340 + 132
= Rs. 472

Ratio of initial investments
$$\eqalign{ & = \frac{1}{3}:\frac{1}{4}:\frac{1}{5} \cr & = 20:15:12 \cr} $$
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
$$\eqalign{ & \therefore {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {4340 \times \frac{4}{{14}}} \right) \cr & = {\text{Rs}}{\text{.1240}} \cr} $$