On a certain sum, the compound interest in 2 years amounts to ₹ 4240. If the rates of interest for successive years are 10% and 15% respectively, find the sum.

Given,

C.I. = ₹ 4240

r₁ = 10%

r₂ = 15%

n = 2 years

Let principal amount be ₹ x.

A = P + C.I. = ₹ x + ₹ 4240

By formula,

A = $P\Big(1 + \dfrac{r$1}{100}\Big)\Big(1 + \dfrac{r2}{100}\Big)

Substituting values we get :

$\Rightarrow x + 4240 = x \times \Big(1 + \dfrac{10}{100}\Big)(1 + \dfrac{15}{100}) \\[1em] \Rightarrow x + 4240 = x \times \dfrac{110}{100} \times \dfrac{115}{100} \\[1em] \Rightarrow x + 4240 = x \times \dfrac{11}{10} \times \dfrac{23}{20} \\[1em] \Rightarrow x + 4240 = \dfrac{253x}{200} \\[1em] \Rightarrow 200(x + 4240) = 253x \\[1em] \Rightarrow 200x + 848000 = 253x \\[1em] \Rightarrow 253x - 200x = 848000 \\[1em] \Rightarrow 53x = 848000 \\[1em] \Rightarrow x = \dfrac{848000}{53} = ₹16000.$

Hence, principal amount = ₹ 16000.