A, B and C started a business. A invests $\frac{1}{2}$ capital for $\frac{1}{4}$ time, B invests $\frac{1}{8}$ capital for $\frac{1}{2}$ time an invests the remaining capital for whole time. Find the share of B in the total profit of $₹ 9900 .$ .

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$₹ 2200$

$₹ 6600$

$₹ 4400$

$₹ 1100$

answer is B.

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Detailed Solution

C's capital $= 1 - (\frac{1}{2} + \frac{1}{8}) = 1 - \frac{5}{8} = \frac{3}{8}$ Ratio of capitals of A. B and C

$\begin{array}{l} = (\frac{1}{2} \times \frac{1}{4}) : (\frac{1}{8} \times \frac{1}{2}) : (\frac{3}{8} \times 1) \\ = \frac{1}{8} : \frac{1}{16} : \frac{3}{8} = 2 : 1 : 6 \end{array}$

B's share $= ₹ (\frac{1}{9} \times 9900) = ₹ 1100$

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