Correct Answer - Option 3 : 14 years
Given:
R and S invested money in the ratio of 4 ∶ 5.
S invested money for one year lesser than the money invested by R.
They earned profits in the ratio of 6 ∶ 7.
Concepts used:
Net capital invested = Time for which capital is invested × capital invested
Calculation:
R and S invested money in the ratio of 4 ∶ 5.
Let capital of R be 4x and capital of S be 5x and time for which capital is invested by R be y years.
⇒ Net capital invested by R = y × 4x = 4xy
⇒ Net capital invested by A = (y – 1) × 5x = 5xy – 5x
Ratio of profits = 4xy ∶ (5xy – 5x) = 4y ∶ (5y – 5)
⇒ 6 ∶ 7 = 4y ∶ (5y – 5)
⇒ 6 × (5y – 5) = 4y × 7
⇒ 30y – 30 = 28y
⇒ 2y = 30
⇒ y = 15 years
⇒ Time for which S invested capital = y – 1 years = 14 years
∴ S invested capital for 14 years.
