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,… — Answer & Discussion

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 ?

A1,200/-
B600/-
C900/-
D300/-

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Discussion 1

CCommunity23 May 2019

Solution
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 = $3 \times 300$
= $Rs. 900$