$P$ and $Q$ enter into a partnership. $P$ puts in $Rs.\ 50$ and $Q$ puts $Rs.\ 45$. At the end of the $4$ months $P$ withdraws half his capital and at the end of $5th$ month $Q$ withdraws half of his capital. $S$ then enter into with the capital of $Rs.\ 70$. At the end of $12$ months they got profit of $Rs.\ 1272.5$. What was $S$ share in the profit.

Using the standard partnership method of multiplying each partner's capital by the time it was invested, P's effective capital is (50 * 4) + (25 * 8) = 400. Q's effective capital is (45 * 5) + (22.5 * 7) = 382.5. S invested 70 for 7 months, making an effective capital of 490. The ratio of their profit shares is 400 : 382.5 : 490, which sums to a total of 1272.5. Since S's ratio value of 490 exactly matches the total profit of 1272.5 divided by itself, S's share in the profit is Rs. 490.

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