P and Q invested in a venture in the ratio 4:7. The profit was shared in the ratio 8:7. If P invested for 14 months, for how long did Q invest?

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1. Let capitals be $4x$ and $7x$. P's time is 14 months and Q's time is $t$.  
2. Profit ratio follows capital × time: $(4x	imes14):(7x	imes t)=8:7$.  
3. So $\dfrac{56}{7t}=\dfrac{8}{7}$. Solve: $56	imes7=8	imes7t\Rightarrow392=56t$.  
4. Thus $t=7$. Q invested 7 months.  
FINAL_ANSWER: b

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