 ### A started a business by investing some money and B invested Rs. 5000 each more than that of A. A remained in business for 5 months and B remained in business 1 month more than A. Out of the total profit of Rs. 26000, B got Rs. 6000 more than A. Find the capitals invested A and B ?

A. Rs. 29000, Rs. 18000 B. Rs. 25000, Rs. 3000 C. Rs. 15000, Rs. 10000 D. Rs. 15000, Rs. 20000 Answer: Option D
Let amount invested by A = Rs. x \begin{aligned}&A&:&B\\ \text{ Capital }\rightarrow\quad&x&:&(x+5000)\end{aligned} $\begin{array}{l}\text{According to the question,}\\ \text{Share of A in profit}\\ =\Large\frac{(26000-6000)}{2}\\ =\text{ Rs. }10000\\ \text{Share of B in profit}\\ =\left(26000-10000\right)\\ =\text{Rs.}\ 16000\end{array}$ $\begin{array}{l}\Large\frac{\mathrm{C}_1\times\mathrm{T}_1}{\mathrm{C}_2\times\mathrm{T}_2}=\frac{\mathrm{P}_1}{\mathrm{P}_2}\\ \Leftrightarrow\Large\frac{x\times5}{(x+5000)\times6}=\frac{10000}{16000}\\ \Leftrightarrow4x=3x+15000\\ \Leftrightarrow x=\mathrm{Rs}.15000\end{array}$ $\begin{array}{l}\text{Required capital of A}\\ =\text{Rs.}\ 15000\\ \text{Required capital of B}.\\ =\left(15000+5000\right)\\ =\text{Rs.}\ 20000\end{array}$