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