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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