### 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

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

A. 5 : 7 : 8
B. 20 : 49 : 64
C. 38 : 28 : 21
D. None of these

A. Rs. 4000
B. Rs. 5000
C. Rs. 6000
D. Rs. 7000

A. Rs. 2380
B. Rs. 2300
C. Rs. 2280
D. Rs. 2260

A. Rs. 40000
B. Rs. 50000
C. Rs. 60000
D. Rs. 70000