Question 31

The ratio of investments of two partners P and Q is 9 : 10 and the ratio of their profits is 4 : 5. If P invested the money for 8 months, then for how much time Q invested his money.

Solution

Assume the P and Q investments are $$9x$$ and $$10x$$ respectively.

And their profits are $$4y$$ and $$5y$$ respectively.

Given that P invested for 8 months

So, $$8\times9x=4y$$

or, $$72x=4y$$

$$y=18x$$ . . . (1)

Now assume that Q invested for $$m$$ months

So, his profit $$5y=m\times10x$$ . . . (2)

put eqn (1) in (2) we get

$$5\times18x=m\times10x$$

$$90x=m\times10x$$

$$m=9$$

Hence, the answer is 9 months.

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