Partnership - Aptitude MCQ Questions and Solutions with Explanations

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,
$$\eqalign{ & \frac{{14x}}{{8y}} = \frac{5}{7} \Rightarrow 98x = 40y \cr & \Rightarrow y = \frac{{49x}}{{20}} \cr & {\text{And, }}\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \Rightarrow 112x = 35z \cr & \Rightarrow z = \frac{{112x}}{{35}} = \frac{{16x}}{5} \cr & {\text{So}}\,x:y:z = x:\frac{{49x}}{{20}}:\frac{{16x}}{5} \cr & ({\text{Multiply by 20}}) \cr & \Rightarrow 20:49:64 \cr} $$

Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A : B : C =6x : 4x : x
= 6 : 4 : 1
B's share = $$16500 \times \frac{4}{{11}}$$   = 1500 × 4 = 6000.

Now as per question, Kamal invested for 12 months and Sameer invested for 7 months.
So Kamal : Sameer = (9000 × 12) : (8000 × 7)
= 108 : 56
= 27 : 14
Sameer Ratio in profit will be
$$\eqalign{ & = {6970 \times \frac{{14}}{{41}}} \cr & = {\text{Rs}}{\text{. 2380}} \cr} $$

Let the amount invested by Q = q.
$$\eqalign{ & 40000:q = 2:3 \cr & \Rightarrow \frac{{40000}}{q} = \frac{2}{3} \cr & \Rightarrow q = 40000 \times \frac{3}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 60000}} \cr} $$

Let
P's capital = p,
Q's capital = q and
R's capital = r.
Then
$$\eqalign{ & 4p = 6q = 10r \cr & \Rightarrow 2p = 3q = 5r \cr & \Rightarrow q = \frac{{2p}}{3} \cr & \Rightarrow r = \frac{{2p}}{5} \cr & {\text{P}}:{\text{Q}}:{\text{R}} = p:\frac{{2p}}{3}:\frac{{2p}}{5} \cr & ({\text{Multiply by 15}}) \cr & = 15:10:6 \cr & {\text{R's share}} = 4650 \times \frac{6}{{31}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 150 \times 6 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}900 \cr} $$

$$\eqalign{ & A:B:C \cr & = \left( {10 \times 7} \right):\left( {12 \times 5} \right):\left( {15 \times 3} \right) \cr & = 70:60:45 \cr & = 14:12:9 \cr & \therefore {\text{C's rent}} = {\text{Rs}}{\text{.}}\left( {175 \times \frac{9}{{35}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}45 \cr} $$

Assume that investment of C = x
Then, investment of A = 2x
Investment of B = $$\frac{{2{\text{A}}}}{3}$$ = $$\frac{{4{\text{x}}}}{3}$$ (since ratio of investment of A : B = 2 : 3 i.e B = $$\frac{{2{\text{A}}}}{3}$$)
A : B : C
= 2x : $$\frac{{4{\text{x}}}}{3}$$ : x
= 2 : $$\frac{4}{3}$$ : 1
= 6 : 4 : 3
$$\eqalign{ & {\text{B's Share}} \cr & = 157300 \times \frac{4}{{6 + 4 + 3}} \cr & = 157300 \times \frac{4}{{13}} \cr & = 12100 \times 4 \cr & = {\text{Rs}}{\text{. 48400}} \cr} $$

A : B : C
= (20,000 × 24) : (15,000 × 24) : (20,000 × 18)
= 4 : 3 : 3.
$$\eqalign{ & {\text{So B's Share}} \cr & = {\text{Rs}}{\text{. }}25000 \times \frac{3}{{10}} \cr & = {\text{Rs}}{\text{. 7500}} \cr} $$

P : Q : R
= (25 × 1 + 35 × 2) : (35 × 2 : 25 × 1) : (30 × 3)
= 95 : 95 : 90
= 19 : 19: 18

Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000
So, x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
$$\eqalign{ & {\text{So A's Share}} \cr & = {\text{Rs}}{\text{. 3}}5000 \times \frac{{21}}{{50}} \cr & = {\text{Rs}}{\text{. 14700}} \cr} $$