Question : On a partnership basis, A and B invested in a ratio of 5 : 6. At the end of 8 months A withdrew his capital. If they shared the eventual profit in the ratio of 5 : 9, then what is the number of months for which B invested his capital?
Option 1: 6 months
Option 2: 10 months
Option 3: 12 months
Option 4: 11 months
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Correct Answer: 12 months
Solution :
A's initial investment is 5$x$ and B's initial investment is $6x$, where $x$ is a positive constant.
after 8 months,
A's effective investment for the entire duration is $5x × 8$
B's effective investment is $6x × t$, where $t$ is the number of months
The total profit is earned for $t$ months.
So, $5x × 8 : 6x × t = 5 : 9$
⇒ $40 : 6t = 5 : 9$
⇒ $t$ = 12
Hence, the correct answer is 12 months.
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