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A and B enter into a partnership with Rs. 50000 and Rs. 60000 respectively. C joins them after x months, contributing Rs. 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: Option A
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Solution(By Apex Team)

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 os A, B, C $\begin{array}{l} =(50000 \times 12):[60000 \times(12-x)]:[70000 \times(12-x)]\\ =60: 6(12-x): 7(12-x)\\ \text { But ratio of profits }\\ =20: 18: 21\\ =60: 54: 63\\ \therefore 60:(72-6 x):(84-7 x)=60: 54: 63\\ \text { So, } 72-6 x=54\\ \Rightarrow 6 x=18\\ \Rightarrow x=3 \end{array}$

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