Multiple choice

A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs. 180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs. 120. For how many years was the sum invested?

  1. 24 years

  2. 22 years

  3. 25 years

  4. 23 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal and T be the time. SI = P * R * T / 100. Amount = P + SI. So, P(1 + 0.08T) = 180 and P(1 + 0.04T) = 120. Dividing the two equations: (1 + 0.08T) / (1 + 0.04T) = 180/120 = 1.5. Solving for T: 1 + 0.08T = 1.5 + 0.06T, which gives 0.02T = 0.5, so T = 25.

AI explanation

Let the principal be P and the time be T years. Using the simple interest formula, the two scenarios give P + (P x 8 x T)/100 = 180 and P + (P x 4 x T)/100 = 120. Subtracting the second equation from the first eliminates P and yields (P x 4 x T)/100 = 60. Substituting this back to find P gives P = 1500/T, and using this in the second equation gives 1500/T + (1500/T x 4 x T)/100 = 120, which simplifies to 1500/T = 60. Therefore, the sum was invested for 25 years.

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