Compound interest on a certain sum of money at 5% per annum for two years is ₹ 246. Calculate simple interest on the same sum for 3 years at 6% per annum.

Let sum of money be ₹ x.

By formula,

$\Rightarrow C.I. = A - P \\[1em] \Rightarrow 246 = P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] \Rightarrow 246 = x \times \Big(1 + \dfrac{5}{100}\Big)^2 - x \\[1em] \Rightarrow 246 = x \times \Big(\dfrac{105}{100}\Big)^2 - x \\[1em] \Rightarrow 246 = x \times \Big(\dfrac{21}{20}\Big)^2 - x \\[1em] \Rightarrow 246 = x \times \dfrac{441}{400} - x \\[1em] \Rightarrow 246 = \dfrac{441x}{400} - x \\[1em] \Rightarrow 246 = \dfrac{441x - 400x}{400} \\[1em] \Rightarrow 246 = \dfrac{41x}{400} \\[1em] \Rightarrow x = \dfrac{246 \times 400}{41} \\[1em] \Rightarrow x = ₹ 2400.$

For S.I. :

P = x = ₹ 2400

R = 6%

T = 3 years

By formula,

$\Rightarrow S.I. = \dfrac{P \times R \times T}{100} \\[1em] \Rightarrow S.I. = \dfrac{x \times 6 \times 3}{100} \\[1em] \Rightarrow S.I. = \dfrac{2400 \times 6 \times 3}{100} \\[1em] \Rightarrow S.I. = ₹ 432.$

Hence, simple interest = ₹ 432.