C and D invested in a business in the ratio 7:9. Their profit ratio was 14:15. If D invested his money for 10 months, for how many months did C invest?

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1. Investments are in ratio $7:9$. Let C's time be $t$ months and D's time be $10$ months.

2. Profit ratio equals investment × time, so $7t : 9	imes10 = 14:15$.

3. Write equation: $\dfrac{7t}{90}=\dfrac{14}{15}$. Solve: $7t=90	imes\dfrac{14}{15}=84$.

4. So $t=\dfrac{84}{7}=12$. C invested for 12 months.

FINAL_ANSWER: b

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