Correct Answer - Option 4 : 2 years
Given:
X, Y and Z invested money for certain time period in the ratio of 10 ∶ 15 ∶ 12.
Y invested Rs. 15,000 more than the money invested by X while X invested Rs. 20,000 less than the money invested by Z.
X and Y invested money for 5 and 3 years respectively.
Concepts used:
Net capital invested = Time for which capital is invested × capital invested
Calculation:
Y invested Rs. 15,000 more than the money invested by X while X invested Rs. 20,000 less than the money invested by Z.
Let the money invested by Z be x.
⇒ Money invested by X = x – 20,000
⇒ Money invested by Y = x – 20,000 + 15,000 = x – 5,000
X and Y invested money for 5 and 3 years respectively.
⇒ Net capital invested by X = 5 × (x – 20,000) = 5x – 1,00,000
⇒ Net capital invested by Y = 3 × (x – 5,000) = 3x – 15,000
Let Z invested capital for y years.
Net capital invested by Z = y × x = xy
Ratio of capital of X, Y and Z = (5x – 1,00,000) ∶ (3x – 15,000) ∶ xy
⇒ 10 ∶ 15 ∶ 12 = (5x – 1,00,000) ∶ (3x – 15,000) ∶ xy
On comparing,
⇒ 10/15 = (5x – 1,00,000)/(3x – 15,000)
⇒ 2 × (3x – 15,000) = 3 × (5x – 1,00,000)
⇒ 6x – 30,000 = 15x – 3,00,000
⇒ 9x = 2,70,000
⇒ x = Rs. 30,000
15/12 = (3x – 15,000)/xy
⇒ 5/4 = (3 × 30,000 – 15,000)/(30000y)
⇒ 5/4 = 75000/30000y
⇒ 5/4 = 5/2y
⇒ y = 2
∴ Z invested money for 2 years.
