Discussion
Two friends invested ₹ 3,000 and ₹ 7,500 in a business. They earned a profit of ₹ 2,800. 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 respectively ?
Answer: C
They received ₹ 1,100 and ₹ 1,700.
Half the profit, ₹ 1,400, is shared equally: ₹ 700 each. The other ₹ 1,400 is shared in the ratio of capitals, \(3000 : 7500 = 2 : 5\):
\[ \begin{aligned} \text{first} &= 1400 \times \tfrac{2}{7} = 400 \\ \text{second} &= 1400 \times \tfrac{5}{7} = 1000 \end{aligned} \]
Totals: \(700 + 400 = 1100\) and \(700 + 1000 = 1700\), which add to the profit of ₹ 2,800. Every option adds to 2,800, so the sum alone does not decide it; only this split gives the right shares.
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