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 ?

Explanation:-

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
$$\eqalign{ & = 18x \times 4 + \left( {18x + 2000} \right) \times 8 \cr & = 72x + 144x + 16000 \cr & = 216x + 16000 \cr}$$
After 4 months, from the start of business,
B invest Rs. 7000 more for each eight months.
Total investment by B
$$\eqalign{ & = 7x \times 4 + \left( {7x + 7000} \right) \times 8 \cr & = 28x + 56x + 56000 \cr & = 84x + 56000 \cr}$$
According to the question,
$$\Rightarrow \frac{{216x + 16000}}{{84x + 56000}} = \frac{2}{1}$$
⇒ 216x + 16000 = 168x + 112000
⇒ 216x - 168x = 112000 - 16000
⇒ 48x = 96000
⇒ x = 2000
Total initial investment of A and B
= (18 + 7) × 2000
= Rs. 50000