Anuj and Rajesh each lent the same sum of money for 2 years at 8% simple interest and compound interest respectively. Rajesh received ₹ 64 more than Anuj. Find the money lent by each and interest received.

Let money lent by both be ₹ x.

For Anuj :

S.I. = $\dfrac{P\times R \times T}{100} = \dfrac{x \times 8 \times 2}{100} = \dfrac{4x}{25}$.

For Rajesh :

C.I. = A - P

$C.I. = P\Big(1 + \dfrac{r}{100}\Big)^n - P \\[1em] = x \times \Big(1 + \dfrac{8}{100}\Big)^2 - x \\[1em] = x \times \Big(\dfrac{108}{100}\Big)^2 - x \\[1em] = x \times \Big(\dfrac{27}{25}\Big)^2 - x \\[1em] = x \times \dfrac{729}{625} - x \\[1em] = \dfrac{729x}{625} - x \\[1em] = \dfrac{729x - 625x}{625} \\[1em] = \dfrac{104x}{625}.$

Given,

Rajesh received ₹ 64 more than Anuj. So, it means Rajesh received ₹ 64 more than Anuj as interest.

$\therefore \dfrac{104x}{625} - \dfrac{4x}{25} = 64 \\[1em] \Rightarrow \dfrac{104x - 100x}{625} = 64 \\[1em] \Rightarrow \dfrac{4x}{625} = 64 \\[1em] \Rightarrow x = \dfrac{625 \times 64}{4} \\[1em] \Rightarrow x = ₹ 10000.$

Calculating S.I. and C.I. :

$S.I. = \dfrac{4x}{25} = \dfrac{4 \times 10000}{25} = ₹ 1600. \\[1em] C.I. = \dfrac{104x}{625} = \dfrac{104 \times 10000}{625} = ₹ 1664.$

Hence, sum of money lent = ₹ 10000 and interest received by Anuj = ₹ 1600 and by Rajesh = ₹ 1664.