Aparna invests money in three different schemes for 6 years, 10 years and 12 years at 10%, 12% and 15% simple interest respectively. At the completion of each scheme, she gets the same interest. The ratio of her investments is:

Given:

Time = 6 yrs, 10 yrs, 12 yrs

Rate = 10%, 12%, 15%

Interest from each scheme is equal

Formula used:

Simple Interest (SI) = \(\dfrac{P × R × T}{100}\)

If SI is same, then \(P ∝ \dfrac{1}{R × T}\)

Calculation:

Investment ratio = \(\dfrac{1}{10 × 6} : \dfrac{1}{12 × 10} : \dfrac{1}{15 × 12}\)

⇒ Investment ratio = \(\dfrac{1}{60} : \dfrac{1}{120} : \dfrac{1}{180}\)

Take LCM of 60, 120, 180 = 360

⇒ Ratio = 360 ÷ 60 : 360 ÷ 120 : 360 ÷ 180

⇒ Ratio = 6 : 3 : 2

∴ The correct answer is 6 : 3 : 2