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Question
On what sum will the difference between compound interest and the simple interest for 2 years at `7 1/2` % be Rs 22.50 ?
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Solution
P = x ; t = 2 years ; r = `7 1/2` % = `15/2` %
For S.I. :
I = `("P" xx "r" xx "t")/100`
`= ("x" xx 15/2 xx 2)/100`
`= (3"x")/20`
For C.I. :
C.I. = `"P" (1 + "r"/100)^"t" - "P"`
`= "x" (1 + (15/2)/100)^2 - "x"`
`= "x" (1 + 15/(2 xx 100))^2 - "x"`
`= "x" (1 + 3/40)^2 - "x"`
= (x × 1.075 × 1.075) -x
= 1.15562S x - x
= 0.155625 x
Given C.I. - S.I. = Rs 22.50
⇒ 0.155625 x - `(3"x")/20 = "Rs" 22.50`
⇒ 0.155625 x - 0.15 x = Rs 22.50
⇒ 0.005625 x = Rs 22.50
⇒ x -Rs 4,000
Hence, sum = Rs 4,000
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