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X, Y and Z started a business, X invested money for 4 months and claims 1/6th of the profit, Y invested money for 6 months and claims 1/4th of the profit and Z invested Rs. 37800 for 8 months. How much money did X invested?

X, Y and Z started a business, X invested money for 4 months and claims 1/6th of the profit, Y invested money for 6 months and claims 1/4th of the profit and Z invested Rs. 37800 for 8 months. How much money did X invested? Correct Answer Rs. 21600

⇒ Profit claimed by Z = 1 – (1/6) – (1/4) = 7/12th

⇒ Ratio of profit claimed by X, Y and Z = (1/6) ∶ (1/4) ∶ (7/12) = 2 ∶ 3 ∶ 7

Given that,

⇒ Ratio of time for which X, Y and Z invested = 4 ∶ 6 ∶ 8 = 2 ∶ 3 ∶ 4

⇒ Ratio of investments of X, Y and Z = (2/2) ∶ (3/3) ∶ (7/4) = 4 ∶ 4 ∶ 7

As, Z invested Rs. 37800,

∴ Amount invested by X = 37800 × (4/7) = Rs. 21600

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