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.