Partnership - Aptitude MCQ Questions and Solutions with Explanations

Let C subscribes the business = Rs. x
A : B : C
Capital → (x + 12000) : (x + 5000) : x
Note: Profit would be divide in the ratio of their capitals
According to the question,
$$\eqalign{ & \Rightarrow \left( {x + 12000} \right) + \left( {x + 5000} \right) + x = 47000 \cr & \Rightarrow 3x + 17000 = 47000 \cr & \Rightarrow 3x = 30000 \cr & \Rightarrow x = 10000 \cr & {\text{ A }}:{\text{ B }}:{\text{ C}} \cr & {\text{Capital}} \to 22000:15000:10000 \cr & {\text{Profit}} \to {\text{ }}22{\text{ }}:{\text{ }}15{\text{ }}:{\text{ }}10 \cr & \left( {22 + 15 + 10} \right){\text{ units}} = {\text{4700}} \cr & {\text{1 unit}} = \frac{{4700}}{{47}} = 100 \cr & {\text{Share of C}} = 10{\text{ units}} = 10 \times 100 = {\text{Rs}}.1000 \cr & \cr} $$

	A		B
Capital →	1850000	:	225000
Profit →	37	:	45
	↓×200	:	↓×200
	7400		9000

Total profit = (7400 + 9000) = Rs. 16400

	A		B
Capital →	35000	:	56000
Profit →	5	:	8
	↓×9000	:	↓×9000
	45000		72000

Total profit = (45000 + 72000) = Rs. 117000

Sonia : Vivek : Sagar
= (60000 × 24) : (140000 × 18) : (120000 × 12)
= 1440000 : 2520000 : 1440000
= 4 : 7 : 4
$$\eqalign{ & \therefore {\text{Vivek's share}} \cr & \Rightarrow {\text{Rs}}{\text{.}}\,\left( {450000 \times \frac{7}{{15}}} \right) \cr & \Rightarrow {\text{Rs}}{\text{. 210000}} \cr} $$

Let the initial capital of P and Q be Rs. 2x and Rs. 3x respectively
Then, ratio of profits
$$\eqalign{ & = \left( {2x \times 12} \right):\left( {3x \times 24} \right) \cr & = 24x:72x \cr & = 1:3 \cr & \therefore {\text{Q's share}} \cr & = {\text{Rs}}{\text{.}}\left( {26000 \times \frac{3}{4}} \right) \cr & = {\text{Rs. }}{\text{19500}} \cr} $$

Let the money invested by A, B and C be Rs. x, Rs. 2x and Rs. 3x respectively
Then, A : B : C
$$\eqalign{ & = \left( {x \times 12} \right):\left( {2x \times 6} \right):\left( {3x \times 4} \right) \cr & = 12x:12x:12x \cr & = 1:1:1 \cr & \therefore {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left( {27000 \times \frac{1}{3}} \right) \cr & = {\text{Rs. }}{\text{9000}} \cr} $$

Let the capitals of Y was used for T months
According to the question,
$$\eqalign{ & \frac{{5 \times 8}}{{6 \times {\text{T}}}}{\text{ = }}\frac{5}{9} \cr & \Rightarrow {\text{T}} = {\text{12 months}} \cr} $$
Hence capital of Y was used for = 12 months

	1st Partner		2nd Partner
Capital →	125000	:	85000
	25	:	17
		8

According to the question,
Note: 60% of profit should be divided equally between them
$$\eqalign{ & {\text{8 units}} = {\text{Rs}}{\text{.}}\,{\text{300}} \cr & {\text{1 unit}} = {\text{Rs}}{\text{.}}\,\frac{{{\text{300}}}}{8} \cr & {\text{42 units}} = {\text{Rs}}{\text{.}}\,\frac{{300 \times 42}}{8} \cr & 40\% {\text{ of profit}} \cr & = {\text{Rs}}{\text{.}}\,\frac{{300 \times 42}}{8} \cr & 100\% {\text{ profit}} \cr & = {\text{Rs}}.\,\frac{{300 \times 42 \times 100}}{{8 \times 40}} \cr & = {\text{Rs}}{\text{.}}\,{\text{3937}}{\text{.50}} \cr} $$

30% of the total profit is divided in the ratio 50000 : 70000 = 5 : 7 between the two partners.
Suppose x = 30% of the total profit. Then
$$\eqalign{ & x \times \frac{{7 - 5}}{{7 + 5}} = 90 \cr & x \times \frac{1}{6} = 90 \cr & x = 540 \cr & 30\% \,{\text{of}}\,{\text{the}}\,{\text{total}}\,{\text{profit}} = 540 \cr & {\text{Total Profit}} \cr & = \frac{{540 \times 100}}{{30}} \cr & = 1800 \cr} $$

Alternative
From the 30% of the profit, let first partner gets x and second partner gets (x + 90)
$$\eqalign{ & x:(x + 90) = 50000:70000 \cr & x:(x + 90) = 5:7 \cr & 7x = 5x + 450 \cr & 2x = 450 \cr & x = 225 \cr & \therefore 30\% \,{\text{of}}\,{\text{the}}\,{\text{profit}} \cr & = x + {\text{x}} + 90 \cr & = 225 + 225 + 90 \cr & = 540 \cr & {\text{Total Profit}} = \frac{{540 \times 100}}{{30}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1800 \cr} $$

A : B : C
(40000 × 36) :(80000 × 12 + 40000 × 24) : (120000 × 24 + 40000 × 12)
= 144 : 192 : 336
= 3 : 4 : 7