A and B enter into a partnership with ₹ 50000 and ₹ 60000 respectively. C joins them after $x$ months, contributing ₹ 70000 and B leaves $x$ months before the end of the year. If they share the profit in the ratio of 20 : 18 : 21, then the value of $x$ is
(a)3
(b)6
(c)8
(d)9
Answer
Answer (as printed): A
Explanation
Clearly, A invested his capital for 12 months while each one of B and C invested his capital for $(12-x)$ months. Ratio of profits of A, B and C $$\begin{aligned} & =(50000 \times 12):[60000 \times(12-x)]:[70000 \times(12-x)] \\ & =60: 6(12-x): 7(12-x) \\ & =60:(72-6 x):(84-7 x) \end{aligned}$$ But ratio of profits $=20: 18: 21=60: 54: 63$. $$\begin{aligned} & \therefore \quad 60:(72-6 x):(84-7 x)=60: 54: 63 \\ & \text { So, } 72-6 x=54 \Rightarrow 6 x=18 \Rightarrow x=3 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.