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Question
On what sum will the difference between compound interest and the simple interest for 3 years at 12% be Rs 1,123.20?
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Solution
P = x ; t = 3 years ; r = 12 % For S.I.:
I = `("P" xx "r" xx "t")/100`
`= ("x" xx 12 xx 3)/100`
`= (9"x")/25`
For C.I. :
C.I. = `"P" (1 + "r"/100)^"t" - "P"`
`= "x" (1 + 12/100)^3 - "x"`
`= "x" (1 + 3/25)^3 - "x"`
= (x × 1.12 × 1.12 × 1.12) - x
=1. 404928x - x
= 0.404928 x
Given C.1.- S. I. = Rs 22.50
⇒ 0.404928 x - `(9"x")/25` = Rs 1123.20
⇒ 0.404928 x - 0.36 x = Rs 1123.20
⇒ 0.044928 x = Rs 1123.20
⇒ x = Rs 25000
Hence, sum = Rs 25,000
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