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Question
The S.I. and C.I. on a sum of money for 2 years is Rs. 200 and 210 respectively. If the rate of interest is the same. Find the sum and rate.
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Solution
Let the sum be P and rate of interest be r % then.
S.I. = `("P" xx "r" xx "n")/(100)`
200 = `("P" xx "r" xx 2)/(100)`
P.r = 10000 ...(i)
C.I. = P `[(1 + r/100)^n - 1]`
210 = `(10000)/r [(1 + r/100)^2 - 1]`
210 = `(10000)/r ((100 + r)^2 - 100^2)/(100)^2`
210 = `(r^2 + 200r)/r`
r2 + 200 r = 210 r
r2 = 10 r
r = 10%
Using this in equation (1), we get
P = `(10000)/(10)`
= ₹ 1000
∴ P = ₹ 1,000
r = 10%
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