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Two friends invested Rs.1500 and Rs. 2500 in a business. They earned a profit of Rs. 800. One-half of the profit was divided equally between them and the other half was divided in proportion to their capitals. How much did each of them receive ?

a) Rs. 350 and Rs. 450
b) Rs. 360 and Rs. 440
c) Rs. 370 and Rs. 430
d) Rs. 375 and Rs. 425

Answer: a
Explanation:
$$\eqalign{ & {\text{Ratio of shares}} = 1500:2500 \cr & = 3:5 \cr & {\text{Share of first friend}} = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{3}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 150} \right) \cr & = {\text{Rs}}{\text{. 350}} \cr & {\text{Share of second friend}} = {\text{Rs}}{\text{.}}\left[ {\frac{{400}}{2} + \left( {400 \times \frac{5}{8}} \right)} \right] \cr & = {\text{Rs}}.\left( {200 + 250} \right) \cr & = {\text{Rs}}{\text{. 450}} \cr} $$

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