###
**A and B started a business with initial investments in the respective ratio of 18 : 7. After 4 months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more. At the end of one year, if the profit was distributed among them in the ratio of 2 : 1 respectively, what was the total initial investment with which A and B started the business ?**

A. Rs. 50000
B. Rs. 25000
C. Rs. 150000
D. Rs. 75000
**Answer: Option A**

## Show Answer

Solution(By Apex Team)

Let the initial investment of A and B is 18x and 7x
After 4 months from the start of business,
A invest Rs. 2000 more for each eight months.
Then total investment of A
$\begin{array}{l}
=18 x \times 4+(18 x+2000) \times 8 \\
=72 x+144 x+16000 \\
=216 x+16000
\end{array}$
After 4 months, from the start of business,
B invest Rs. 7000 more for each eight months.
Total investment by B
$\begin{array}{l}
=7 x \times 4+(7 x+7000) \times 8 \\
=28 x+56 x+56000 \\
=84 x+56000
\end{array}$
According to the question,
$\begin{array}{l}\Rightarrow\Large\frac{216x+16000}{84x+56000}=\frac{2}{1}\\
\Rightarrow216x+16000=168x+112000\\
\Rightarrow216x-168x=112000-16000\\
\Rightarrow48x=96000\\
\Rightarrow x=2000\end{array}$
Total initial investment of A and B
$\begin{array}{l}
=(18+7) \times 2000 \\
=\text { Rs. } 50000
\end{array}$

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