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P and Q invested money in the ratio of 2 ∶ 3. Q invested money for two years lesser than the money invested by P. They earned profits in the ratio of 4 ∶ 5. Find the time for which Q invested the money.


1. 10 years
2. 12 years
3. 15 years
4. 20 years

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Best answer
Correct Answer - Option 1 : 10 years

Given:

P and Q invested money in the ratio of 2 ∶ 3.

Q invested money for two years lesser than the money invested by P.

They earned profits in the ratio of 4 ∶ 5.

Concepts used:

Net capital invested = Time for which capital is invested × capital invested

Calculation:

P and Q invested money in the ratio of 2 ∶ 3.

Let capital of P be 2x and capital of Q be 3x and time for which capital is invested by P be y years.

⇒ Net capital invested by P = y × 2x = 2xy

⇒ Net capital invested by Q = (y – 2) × 3x = 3xy – 6x

Ratio of profits = 2xy ∶ (3xy – 6x) = 2y ∶ (3y – 6)

⇒ 4 ∶ 5 = 2y ∶ (3y – 6)

⇒ 4 × (3y – 6) = 2y × 5

⇒ 12y – 24 = 10y

⇒ 2y = 24

⇒ y = 12 years

⇒ Time for which Q invested capital = y – 2 years = 12 – 2 years = 10 years

Q invested capital for 10 years.

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