Kamala borrowed from rattan a certain sum at 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.

Explanation

Simple interest = Rs. 200
Compound interest = Rs. 210
Time`= 2` years
SI for one year`=Rs.2002=Rs.100`
CI for first year = Rs. 100
CI for second year`= Rs.210-100=Rs. 110`
Difference`=Rs.110-Rs.100=Rs.10`
`therefore Rs.10` in S.I. on `Rs.100` for `1` year
`therefore` Rate of interest`=(S.Itimes100)/(PtimesT)`
`(10times100)/(100times1)=10%` per annum
And Principal`=(S.I.times100)/(RtimesT)`
`=(200times100)/10times2=Rs.1000`
Hence, the sum is `Rs.1000` and the rate is `10%` per annum.