A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew $$\frac{1}{4}$$ of his capital and B withdrew $$\frac{1}{5}$$ of his capital. The gain at the end of 10 months was Rs. 760. A’s share in this profit is:
a) Rs. 360
b) Rs. 330
c) Rs. 430
d) Rs. 380
Answer: b
Explanation:
$$A:B$$
$$ = \left[ {4x \times 3 + \left( {4x – \frac{1}{4} \times 4x} \right) \times 7} \right]$$ $$:$$ $$\left[ {5x \times 3 + \left( {5x – \frac{1}{5} \times 5x} \right) \times 7} \right]$$
$$\eqalign{
& = \left( {12x + 21x} \right):\left( {15x + 28x} \right) \cr
& = 33x:43x = 33:43 \cr
& \therefore {\text{A’s share}} = {\text{Rs}}{\text{.}}\left( {760 \times \frac{{33}}{{76}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,330 \cr} $$
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