Question

Kamala borrowed from Ratan a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years, she received Rs. 210 as compound interest, but paid Rs. 200 only as simple interest. Find the sum and the rate of interest.

Answer 1

Simple interest = Rs. 200
and compound interest = Rs. 210
Period = 2 years
Now S.I. for one year $=Rs.\frac{200}{2}=Rs.100$
and C.I. for first year = Rs. 100
and C.I. for second year = Rs. 210 - 100
= Rs. 110
$\therefore$ Difference = Rs. 110 - Rs. 100 = Rs. 10
$\therefore$ Rs. 10 in S.I. on RS. 100 for 1 year
$\therefore$ Rate of interest $=\frac{S.I\times 100}{P\times T}$
$=\frac{10\times 100}{100\times 1}=10\%$ p.a.
and Principal $=\frac{S.I\times 100}{R\times T}$
$=\frac{200\times 100}{10\times 2}=Rs.1000$