Question : Raman, Rohit, and Raja are partners and invest in a business. Raman invests $\frac{1}{4}$th of the total and Rohit invests $\frac{1}{3}$rd of the total. What is the ratio of profit of Raman, Rohit, and Raja respectively?
Option 1: 4 : 3 : 1
Option 2: 3 : 4 : 4
Option 3: 3 : 4 : 5
Option 4: 4 : 3 : 5
Correct Answer: 3 : 4 : 5
Solution :
Raman's share = $\frac{1}{4}$
Rohit's share = $\frac{1}{3}$
Raja's share = $1-(\frac{1}{4}+\frac{1}{3})=\frac{5}{12}$
Share of Raman : Rohit : Raja = $\frac{1}{4}$ : $\frac{1}{3}$ : $\frac{5}{12}$
LCM of 4, 3, and 12 is 12.
Multiplying by 12 in all fractions, we get,
Share of Raman : Rohit : Raja = 3 : 4 : 5
Since the ratio of profit is equal to the ratio of investment for equal time, the share of profit of Raman : Rohit : Raja = 3 : 4 : 5
Hence, the correct answer is 3 : 4 : 5.
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