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### Question

P and Q start a business with investments in the ratio 3 : 16. After 3 months, P increases his capital by $1/3$^{th}, and Q increases his capital by $1/16$^{th}. If the profit at the end of 10 months is 612, then what is the share of P?

**A**

Rs. 111.

**B**

Rs. 211.

**C**

Rs. 11.

**D**

Rs. 311.

**Soln.**

**Ans: a**

After 3 months, the ratio of their capitals is 4:17. The ratio of money-months of P and Q is ${3 × 3 + 4 × 7}/{16 × 3 + 17 × 7}$, which is $37/167$. Profit of P = $37/{37 + 167}$ × 612 = Rs. 111.