P and Q start a business. P invests 3 times the capital of Q. After 7 months, P withdraws one-third of his capital, and Q doubles his capital. If the total duration of the business is 12 months and the total profit is ₹60,000, find Q's share.

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Accepted Answer

1. Let Q's capital be $x$. Then P's capital = $3x$.

2. For P: first 7 months $3x	imes7=21x$, last 5 months after withdrawing $\frac{1}{3}$ he has $2x$, so $2x	imes5=10x$. Total P = $31x$.

3. For Q: first 7 months $x	imes7=7x$, last 5 months after doubling he has $2x$, so $2x	imes5=10x$. Total Q = $17x$.

4. Ratio P:Q = $31:17$. Q's share = $60000	imes\dfrac{17}{31+17}=60000	imes\dfrac{17}{48}=1250	imes17=21250$.

FINAL_ANSWER: b

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