A, B and C start a business. A invests 3 times as much as B, and B invests \(\displaystyle\frac{2}{3}\) of what C invests. At the end of the year they make a profit of Rs 13,200. Find C’s share in the profit.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 3,600
Write all three investments in terms of one of them; for the same time, profit is shared in the ratio of the investments.
Let C invest \(3x\); then B invests \(\frac{2}{3}\times3x=2x\) and A invests \(3\times2x=6x\)
A : B : C \(=6:2:3\), total 11 parts
C’s share \(\displaystyle =\frac{3}{11}\times13200=\) Rs 3,600
C’s share is Rs 3,600.
Why the other options are incorrect
Option (1) Rs 4,400 — Incorrect. This splits the profit equally; it must be shared in the ratio of the investments.
Option (2) Rs 7,200 — Incorrect. This is A’s share, not C’s.
Option (3) Rs 2,400 — Incorrect. This is B’s share, not C’s.