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

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