A, B and C started a business with investments of 1,600/-, 2,100/- and 1,500/- respectively. After 8 months from the start of the business, B and C invested additional amounts in the ratio of 3 : 5 respectively. If the respective ratio between total annual profit and C’s share in the annual profit was 3 : 1, what was the additional amount invested by B after 8 months ?

Let additional amount invested by B = $$Rs. 3x$$

=> Additional amount invested by C = $$Rs. 5x$$

Ratio of profits of A, B and C

= $$[1600 \times 12]$$ : $$[2100 \times 8 + (2100 + 3x) \times 4]$$ : $$[1500 \times 8 + (1500 + 5x) \times 4]$$

= $$(4800) : (4200 + 2100 + 3x) : (3000 + 1500 + 5x)$$

= $$(4800) : (6300 + 3x) : (4500 + 5x)$$

=> Total profit = $$(4800) + (6300 + 3x) + (4500 + 5x)$$

= $$15600 + 8x$$

Acc to ques, ratio of total profit to C's share in the profit

=> $$\frac{15600 + 8x}{4500 + 5x} = \frac{3}{1}$$

=> $$15600 + 8x = 13500 + 15x$$

=> $$15x - 8x = 15600 - 13500$$

=> $$x = \frac{2100}{7} = 300$$

$$\therefore$$ Additional amount invested by B = $$3 \times 300$$

= $$Rs. 900$$