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 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?

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Accepted Answer

Let the additional investments after 8 months be B = $3k$ and C = $5k$ (ratio 3:5).

Compute time-weighted contributions (investment × months):
- A: $1600	imes12=19200$.
- B: $2100	imes8+(2100+3k)	imes4=2100	imes12+12k=25200+12k$.
- C: $1500	imes8+(1500+5k)	imes4=1500	imes12+20k=18000+20k$.

Total profit proportional to $T=19200+(25200+12k)+(18000+20k)=62400+32k$.

Given the ratio total : C = $3:1$, so $T=3	imes$(C share):

$62400+32k=3(18000+20k)=54000+60k$.

Solve for $k$:
$62400-54000=60k-32k\Rightarrow8400=28k\Rightarrow k=300$.

B's additional amount $=3k=3	imes300=900$. Thus the correct option is C.

FINAL_ANSWER: c

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