A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25:8. The rate of interest per annum is (a) 10% (b) 11% (c) 12% (d) `12 1/2%`

Options

A. 0.1
B. 0.11
C. 0.12
D. `12""1/2%`

Answer

D

Explanation

Let the principal be ₹ O and rate of interest be R% oper annum.
Difference of C.I. and S.I for 3 years
`= [ P xx (1 xx R/100)^(3) -P] - ((P xx R xx 3)/100) = (PR^(2))/10^(4) = ((300 + R)/100)`
Difference of C.I. and S.I. for 2 years = ` P ( R/100)^(2)`
` ((PR^(2))/10^(4)((300+R)/100))/((PR^(2))/10^(4)) = 25/8 Rightarrow ((300 + R)/100) = 25/8`
` Rightarrow R = 100/8 = 12""1/2% `