Pramod and Anand each lent the same sum of money for 2 years at 5% at simple interest and compound interest respectively. Anand received ₹ 15 more than Pramod. Find the amount of money lent by each and the interest received.

Let sum of money be ₹ x.

For Pramod :

P = ₹ x

Time = 2 years

Rate = 5%

S.I. = $\dfrac{P \times R \times T}{100}$

Substituting values we get :

$S.I. = \dfrac{x \times 5 \times 2}{100} \\[1em] = \dfrac{x}{10}.$

For Anand :

P = ₹ x

Time (n) = 2 years

Rate (r) = 5%

C.I. = A - P

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

Given,

Anand received ₹ 15 more than Pramod.

∴ C.I. - S.I. = ₹ 15

$\Rightarrow \dfrac{41x}{400} - \dfrac{x}{10} = 15 \\[1em] \Rightarrow \dfrac{41x - 40x}{400} = 15 \\[1em] \Rightarrow \dfrac{x}{400} = 15 \\[1em] \Rightarrow x = 400 \times 15 = ₹ 6000. \\[1em] S.I. = \dfrac{x}{10} = \dfrac{6000}{10} = ₹ 600. \\[1em] C.I. = \dfrac{41x}{400} = \dfrac{41 \times 6000}{400} = ₹ 615.$

Hence, sum lent by each = ₹ 6000 and interest received by Pramod = ₹ 600 and Anand = ₹ 615.