Question : S, T, and U start a business and their capitals are in the ratio of $3:4:6$. At the end, they receive the profit in the ratio of $1:2:3$. What will be the respective ratio of time for which they contribute their capital?
Option 1: $3:2:2$
Option 2: $2:3:3$
Option 3: $2:2:3$
Option 4: $4:5:3$
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Correct Answer: $2:3:3$
Solution : Given: The ratio of profit of S, T, and U = $1:2:3$ Let the capital of S, T, and U be $3x$, $4x$ and $6x$ respectively. Let the time of investment of S, T, and U be $a$, $b$, and $c$ respectively. $3ax:4bx:6cx = 1:2:3$ ⇒ $\frac{3a}{4b}=\frac{1}{2}$ and $\frac{4b}{6c}=\frac{2}{3}$ ⇒ $\frac{a}{b}=\frac{2}{3}$ and $\frac{b}{c}=\frac{1}{1}=\frac{3}{3}$ So, $a:b:c = 2:3:3$. Hence, the correct answer is $2:3:3$
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