X and Y started a business with investments in the ratio 5: 4. After 8 months, X withdrew his entire amount. If the profit at the end of the year was shared in the ratio 5: 9, for how many months did Y invest his money?

Solution

Solution: Profit is proportional to investment × time. Let the investments be \(5x\) and \(4x\), and Y's investment duration be t months. \(\frac{5x\times8}{4x\times t}=\frac59\Rightarrow\frac{40}{4t}=\frac59\Rightarrow t=18\) months. Trick: Compare capital-months to the profit ratio. Source note: The green-marked answer is 18 months, but this exceeds the stated one-year period, so the original question appears inconsistent.