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Question
The difference between C.I. and S.I. on Rs. 7,500 for two years is Rs. 12 at the same rate of interest per annum. Find the rate of interest.,
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Solution
Given: P = Rs. 7,500 and Time (n) = 2 years
Let rate of interest = y%
∴ S.I. = `[ "P" xx "R" xx "T" ]/100`
= `[7500 xx y xx 2]/100`
= Rs. 150y
∴ C.I. = P`(1 + r/100)^n - "P"`
= `"Rs". 7,500( 1 + y/100 )^2 - "Rs." 7,500`
Given: C.I. : S.I. = Rs. 12
⇒ `7,500[ 1 + y/100 ]^2 - 7,500 - 150y = 12`
⇒ `7,500[ 1 + y^2/10000 + (2y)/100 ] - 7,500 - 150y = 12`
⇒ `7,500 + [7500y^2]/[10000] + 150y - 7,500 - 150y = 12`
⇒ `(3y^2)/4 = 12`
⇒ y2 = 16
⇒ y = 4%
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