Question
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 he 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 :
Answer: Option D
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Let the principal be Rs. P and rate of interest be R% per annum.
Difference of C.I. and S.I. for 2 years
=`[P xx (1 + R/100)^2 - P] - ((P xx R xx 2)/(100)) = (PR^2)/(104)`
Difference of C.I. and S.I. for 3 years.
= `[P xx (1 + R/100)^3 - P] - ((P xx R xx 2)/(100)) ` = `(PR^2)/(10^4)((300 + R)/(100))`
`:.` `((PR^2)/(10^4)((300 +R)/(100)))/((PR^2)/(10^4)) = 25/8`
`rArr ((300 + R)/(100)) = 25/8`
`rArr R = 100/8` = `12 1/2`%
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