A starts business with a capital of Rs. 14000. Five months later B joins and further two months later C joins them. If the profit sharing ratio in the end of year is 4 : 3 : 2, then the money invested by C was ?

1Rs. 18000
2Rs. 16800
3Rs. 18600
4Rs. 10800

Answer:- 1

Explanation:-

Solution:

	A	B	C
Amounts invested	14000
Time (in months)	12	7	5
	168000

\begin{aligned} Ratio of profits 4 : 3 : 2 \\ Let their profits 4 x : 3 x : 2 x \\ \Leftrightarrow 4 x = 168000 \\ \Leftrightarrow x = 42000 \\ \Rightarrow Profit share of C \\ = 2 x \\ = 2 \times 42000 \\ = Rs . 84000 \\ \Rightarrow Capital invested by C \\ = \frac{84000}{5} \\ = Rs. 16800 \end{aligned}

$\eqalign{ & {\text{Ratio of profits }}4:3:2 \cr & {\text{Let their profits }}4x:3x:2x \cr & \Leftrightarrow 4x = 168000 \cr & \Leftrightarrow x = 42000 \cr & \Rightarrow {\text{Profit share of C}} \cr & = 2x \cr & = 2 \times 42000 \cr & = {\text{Rs}}{\text{. 84000}} \cr & \Rightarrow {\text{Capital invested by C}} \cr & = \frac{{84000}}{5} \cr & = {\text{Rs. }}16800 \cr}$