A and B started a business with initial investments in the respective ratio of 18 : 7. After four 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?

Let amount invested by A = $$Rs. 18x$$

=> Amount invested by B = $$Rs. 7x$$

After four months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more

Thus, ratio of profit received by A : B

= $$[(18x \times 4) + (18x + 2000) \times 8] : [(7x \times 4) + (7x + 7000) \times 8]$$

= $$(72x + 144x + 16000) : (28x + 56x + 56000)$$

= $$(216x + 16000) : (84x + 56000) = (54x + 4000) : (21x + 14000)$$

Acc. to ques, => $$\frac{54x + 4000}{21x + 14000} = \frac{2}{1}$$

=> $$54x + 4000 = 42x + 28000$$

=> $$54x - 42x = 12x = 28000 - 4000 = 24000$$

=> $$x = \frac{24000}{12} = 2000$$

$$\therefore$$ Total initial investment = $$18x + 7x = 25x$$

= $$25 \times 2000 = Rs. 50,000$$