Partnership - Aptitude MCQ Questions and Solutions with Explanations

Let their initial investments be x, 3x and 5x respectively
Then,
$$ = {\text{A}}:{\text{B}}:{\text{C}}$$
$$ = \left( {x \times 4 + 2x \times 8} \right)$$     : $$\left( {3x \times 4 + \frac{{3x}}{2} \times 8} \right)$$     : $$\left( {5x \times 4 + \frac{{5x}}{2} \times 8} \right)$$
$$\eqalign{ & = 20x:24x:40x \cr & = 5:6:10 \cr} $$

$$\eqalign{ & {\text{Suppose, }} \cr & {\text{A invests Rs}}{\text{.}}\frac{x}{6}{\text{ for }}\frac{y}{6}{\text{ months}} \cr & {\text{Then,}} \cr & {\text{ B invests Rs}}{\text{.}}\frac{x}{3}{\text{ for }}\frac{y}{3}{\text{ months}} \cr & {\text{C invests}}\left[ {x - \left( {\frac{x}{6} + \frac{x}{3}} \right)} \right]i.e.,{\text{ Rs}}{\text{.}}\frac{x}{2}{\text{ for }}y{\text{ months}} \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}} \cr & {\text{ = }}\left( {\frac{x}{6} \times \frac{y}{6}} \right):\left( {\frac{x}{3} \times \frac{y}{3}} \right):\left( {\frac{x}{2} \times y} \right) \cr & = \frac{1}{{36}}:\frac{1}{9}:\frac{1}{2} \cr & = 1:4:18 \cr & {\text{Hence, B's share}} \cr & = {\text{Rs}}{\text{. }}\left( {4600 \times \frac{4}{{23}}} \right) \cr & = {\text{Rs}}{\text{. 800}} \cr} $$

	A	B	C
Amounts invested	14000
Time (in months)	12	7	5
	168000

$$\eqalign{ & {\text{Ratio of profits }}4:3:2 \cr & {\text{Let their profits }}4x:3x:2x \cr & \Leftrightarrow 4x = 168000 \cr & \Leftrightarrow x = 42000 \cr & \Rightarrow {\text{Profit share of C}} \cr & = 2x \cr & = 2 \times 42000 \cr & = {\text{Rs}}{\text{. 84000}} \cr & \Rightarrow {\text{Capital invested by C}} \cr & = \frac{{84000}}{5} \cr & = {\text{Rs. }}16800 \cr} $$

Let the total capital of A, B and C = 15 units
Let total time for investment = 12 units
Now, According to the question,

Capital Investment of A = $$\frac{1}{3} \times 15$$   = 5units
Capital Investment of B = $$\frac{1}{5} \times 15$$   = 3units
Capital Investment of C = 15 - (5 + 3) = 7

A's Capital Invested for time = $$\frac{1}{4} \times 12$$   = 3units
B's Capital Invested for time = $$\frac{1}{6} \times 12$$   = 2units
C's Capital Invested all the time. i.e = 12units

∴ Profit ratio of A : B : C = (5 × 3) : (3 × 2) : (7 × 12)
= 15 : 6 : 84
= 5 : 2 : 28
Total profit = 5 + 2 + 28 = 35 units
Also, total profit = Rs. 1820 (given)
$$\eqalign{ & {\text{35 units}} = {\text{Rs}}{\text{. 1820}} \cr & {\text{1 unit}} = \frac{{1820}}{{35}} = {\text{Rs}}.52 \cr & {\text{Hence A's share in profit}} \cr & = 5{\text{ units}} \cr & = 52 \times 5 \cr & = {\text{Rs}}{\text{. 260}} \cr} $$

Let C's capital be Rs. x
Then,
A : B : C = 2560 : 2000 : x
$$\eqalign{ & {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left( {1105 \times \frac{{2560}}{{4560 + x}}} \right) \cr & \therefore 1105 \times \frac{{2560}}{{4560 + x}} = 320 \cr & \Rightarrow 320x + 1459200 = 2828800 \cr & \Rightarrow 320x = 1369600 \cr & \Rightarrow x = 4280 \cr} $$

$$\eqalign{ & {\text{Let total capital}} = {\text{Rs}}{\text{.}}\,{\text{x}} \cr & {\text{Then, A's capital}} = {\text{Rs}}{\text{.}}\,\frac{x}{3} \cr} $$
B's capital = (A + C)'s capital ⇒ 2(B's capital)
B's capital = (A + B + C)'s capital = Rs. x
$$\eqalign{ & \Rightarrow {\text{B's capital}} = {\text{Rs}}{\text{.}}\frac{x}{2} \cr & \Rightarrow {\text{C's capital}} \cr & = {\text{Rs}}{\text{.}}\left[ {x - \left( {\frac{x}{3} + \frac{x}{2}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\,\frac{x}{6} \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}} \cr & = \frac{x}{3}:\frac{x}{2}:\frac{x}{6} \cr & = 2:3:1 \cr & {\text{So C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {900 \times \frac{1}{6}} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{150}} \cr} $$

Suppose B invested Rs. x for y months
Then, A invested Rs. 3x for 2y months
$$\eqalign{ & {\text{So, A}}:{\text{B}} \cr & = \left( {3x \times 2y} \right):\left( {x \times y} \right) \cr & = 6xy:xy \cr & = 6:1 \cr & \therefore {\text{B's profit}}:{\text{Total profit}} = 1:7 \cr & {\text{Let the total profit is Rs}}{\text{. }}x \cr & {\text{Then,}}\frac{1}{7} = \frac{{4000}}{x} \cr & \Leftrightarrow x = 28000 \cr} $$

$$\eqalign{ & {\text{Suppose B joined for }}x{\text{ months}} \cr & {\text{Then,}} \cr & \Rightarrow \frac{{85000 \times 12}}{{42500 \times x}} = \frac{3}{1} \cr & \Rightarrow x = \frac{{85000 \times 12}}{{42500 \times 3}} \cr & \Rightarrow x = 8 \cr & {\text{So, B joined for 8 months}} \cr} $$

$$\eqalign{ & {\text{Let the total share}} = {\text{200 units}} \cr & \therefore {\text{Share of C}} = 200 \times \frac{1}{4} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 50{\text{ units}} \cr & {\text{Remaining share}} \cr & = \left( {200 - 50} \right) \cr & {\text{ = 150 units}} \cr & \therefore {\text{Share of A}} = \frac{{200}}{{3 + 2}} \times 3 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 120{\text{ units}} \cr & {\text{Share of B}} = \frac{{200}}{{3 + 2}} \times 2 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 80{\text{ units}} \cr} $$
According to the question,
C received equal amounts from A and B
$$\eqalign{ & \therefore {\text{A's remaining share}} \cr & = \left( {120 - 25} \right) \cr & = 95 \cr & {\text{B's remaining share}} \cr & = \left( {80 - 25} \right) \cr & = 55 \cr} $$

	A	:	B	:	C
New Ratio →	95	:	55	:	50
	19	:	11	:	10

	A	:	B	:	C
Ratio of Profit →	2	:	3	:	7

$$\eqalign{ & {\text{Average gain}} = \frac{{2 + 3 + 7}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4{\text{ units}} \cr & {\text{According to the question,}} \cr & {\text{4 units}} = {\text{Rs}}{\text{. 8000}} \cr & {\text{1 unit}} = {\text{Rs}}{\text{. 2000}} \cr & {\text{3 units}} = 3 \times 2000 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 6000}} \cr & \therefore {\text{Share of B}} = {\text{Rs}}{\text{. 6000}} \cr} $$