Question : P, Q, and R are partners and invest in a business. P invests $\frac{1}{5}^{th}$ of total investments and Q invests $\frac{1}{4}^{th}$ of the total investments. What is the ratio of investments of P, Q, and R respectively?
Option 1: 4 : 8 : 11
Option 2: 4 : 5 : 11
Option 3: 4 : 7 : 11
Option 4: 4 : 5 : 9
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Correct Answer: 4 : 5 : 11
Solution : P invests $\frac{1}{5}$th of the total investment. Q invests $\frac{1}{4}$th of the total investment. Taking, LCM (4, 5) = 20 Let the total investment be Rs. 20 P invests $\frac{1}{5}$th of the total investment = $\frac{1}{5}\times 20$ = Rs. 4 Q invests $\frac{1}{4}$th of the total investment = $\frac{1}{4}\times 20$ = Rs. 5 Thus R invests = Rs. 20 – (Rs. 4 + Rs. 5) = Rs. 20 – Rs. 9 = Rs. 11 Thus the ratio of the profit of P, Q, and R respectively is 4 : 5 : 11. Hence, the correct answer is 4 : 5 : 11.
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