S, T and U started 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 period for which they contributed their capitals?
Let the respective time period for which S, T and U contributed their capitals = $$x:y:z$$
Ratio of capitals = $$3:4:6$$
=> Ratio of profit = $$3x:4y:6z=1:2:3$$
=> $$\frac{3x}{4y}=\frac{1}{2}$$
=> $$\frac{x}{y}=\frac{2}{3}$$
Similarly, $$\frac{4y}{6z}=\frac{2}{3}$$
=> $$y=z$$
$$\therefore$$ $$x:y:z=2:3:3$$
=> Ans - (B)
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