If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ), then out of the total profit of Rs. 4650 , R will receive

Answer: Option D

Let
P's capital = p,
Q's capital = q and
R's capital = r.
Then
$$\begin{array}{rl}& 4p=6q=10r\\ & \Rightarrow 2p=3q=5r\\ & \Rightarrow q=\frac{2p}{3}\\ & \Rightarrow r=\frac{2p}{5}\\ & \text{P}:\text{Q}:\text{R}=p:\frac{2p}{3}:\frac{2p}{5}\\ & (\text{Multiply by 15})\\ & =15:10:6\\ & \text{R’s share}=4650\times \frac{6}{31}\\ & =150\times 6\\ & =\text{Rs}\text{. }900\end{array}$$