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1. 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

Solution:

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

= (50000 \times 12)

[60000 \times (12 - x)]

[70000 \times (12 - x)]

\begin{aligned} = 60 : 6 (12 - x) : 7 (12 - x) \\ But ratio of profits \\ = 20 : 18 : 21 \\ = 60 : 54 : 63 \end{aligned}

∴ 60 : (72 - 6 x) : (84 - 7 x)

60

54

63

\begin{aligned} So, 72 - 6 x = 54 \\ \Rightarrow 6 x = 18 \\ \Rightarrow x = 3 \end{aligned}

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