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1. 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

Solution:

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{aligned} = 18 x \times 4 + (18 x + 2000) \times 8 \\ = 72 x + 144 x + 16000 \\ = 216 x + 16000 \end{aligned}

After 4 months, from the start of business,
B invest Rs. 7000 more for each eight months.
Total investment by B

\begin{aligned} = 7 x \times 4 + (7 x + 7000) \times 8 \\ = 28 x + 56 x + 56000 \\ = 84 x + 56000 \end{aligned}

According to the question,

\Rightarrow \frac{216 x + 16000}{84 x + 56000} = \frac{2}{1}

⇒ 216x + 16000 = 168x + 112000
⇒ 216x - 168x = 112000 - 16000
⇒ 48x = 96000
⇒ x = 2000
Total initial investment of A and B
= (18 + 7) × 2000
= Rs. 50000

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