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