In a partnership, A invests \(\frac{1}{6}\) of the total capital for \(\frac{1}{6}\) of the time, B invests \(\frac{1}{3}\) of the total capital for \(\frac{1}{3}\) of the time, and C invests the rest of the capital for the whole time. Out of a profit of Rs 2,300, find the difference between the shares of A and B.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 300
Profit is shared in the ratio of capital × time; here both are given as fractions of the whole.
C’s capital \(\displaystyle =1-\frac{1}{6}-\frac{1}{3}=\frac{1}{2}\)
A : B : C \(\displaystyle =\frac{1}{6}\times\frac{1}{6}:\frac{1}{3}\times\frac{1}{3}:\frac{1}{2}\times1=\frac{1}{36}:\frac{1}{9}:\frac{1}{2}\)
Multiplying by 36: \(1:4:18\), total 23 parts
One part \(\displaystyle =\frac{2300}{23}=\) Rs 100
A \(=\) Rs 100, B \(=\) Rs 400, difference \(=400-100=\) Rs 300
The difference between the shares of A and B is Rs 300.