# P invests Rs. 10000 at the rate of interest 24% on simple interest for M years. He also invests Rs. 12000 at the rate of interest 15% compounded annua

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P invests Rs. 10000 at the rate of interest 24% on simple interest for M years. He also invests Rs. 12000 at the rate of interest 15% compounded annually for N years. He received a total profit of Rs. 13470. The ratio between M and N is 2 : 1. What will be the difference between their time period?
1. 1 year
2. 3 years
3. 4 years
4. 2 years

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Correct Answer - Option 4 : 2 years

Given:

Amount invested on simple interest = Rs. 10000

Formula:

Let P = principal, R = rate of interest and N = time period

Simple Interest = PNR / 100

Compound interest = P(1 + R / 100)n – P

Calculation:

Simple Interest earned in M years = 10000 × 24 × M / 100 = Rs. 2400M

Compound interest earned in N years = 12000(1 + 15 / 100)N – 12000

⇒ M / N = 2 / 1

⇒ M = 2N

⇒ 2400M + 12000(1 + 15 / 100)N – 12000 = 13470

⇒ 4800N + 12000(1 + 15 / 100)N – 12000 = 13470

Using trial and error,

N = 2 years and M = 4 years

Required difference = 4 – 2 = 2 years