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Question

In a partnership, $$A$$ invests $$\dfrac{1}{6}$$ of the capital for $$\dfrac{1}{6}$$ of the time. $$B$$ invests $$\dfrac{1}{3}$$ of the capital for $$\dfrac{1}{3}$$ of the time and $$C$$ rest of the capital for whole time.Find $$B'$$s share out of a profit of Rs,$$4,600$$.


Solution

Let x be the total capital invested
Given: $$\dfrac{1}{6}$$ of the capital is invested by A
Hence A's investment is $$\dfrac{x}{6}$$ for $$\dfrac{T}{6}$$ of time.
Hence total value of A's investment for period $$T/6=x T/36$$
Given: $$\dfrac{1}{3}$$ of the capital is invested by b.
Hence 'b's investment is $$x/3$$ for $$T/3$$ of time.
Hence, total value of b's investment for period $$T/3$$ will be $$Tx/9$$
Rest of the investment is done by c
Hence c's investment is $$x-\dfrac{x}{3}-\dfrac{x}{6}=\dfrac{x}{2}$$ for period of T.
Hence total value of c's investment for period of T will be $$x T/2$$
profit should be divided in the total value of investment for period of $$T=\left(\dfrac{xT}{36}+\dfrac{xT}{9}+\dfrac{xT}{2}\right)=\dfrac{23xT}{36}$$
Hence, B's share should be $$\dfrac{xT}{9}/23x T/36=\dfrac{4}{23}rd$$
Hence, profit received by $$B=\dfrac{4}{23}\times 4600=$$Rs. $$800$$.

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Mathematics

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