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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
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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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