# A sum of money is invested at C.I. payable annually. The interest in two successive years is 225 and 240. Find the rate of interest and original sum

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by Ritvikrai

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by Ritvikrai

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Amount after 1 year = A = P (1 +r/100)^1 = P (1 + r/100)

Interest = P r /100 = 225

=> P r = 22,500 --- equation 1

Amount after 2 years = B = P(1+r/100)^2 = A (1 + r/100)

Interest during 2nd year = B - A = A r /100 = 240

A r = 24 000 -- equation 2

Hence P (1 + r/100) r = 24 000, now substitute Pr from equation 1

(1 + r/100 ) = 24 000 / 22 500

r /100 = 0.0667

* r = 6.67 % per annum*

* P = 22 500 / r = Rs 3, 375 *

amount after 1 year = Rs 3 600

amount after 2 nd year = Rs 3, 840

Interest = P r /100 = 225

=> P r = 22,500 --- equation 1

Amount after 2 years = B = P(1+r/100)^2 = A (1 + r/100)

Interest during 2nd year = B - A = A r /100 = 240

A r = 24 000 -- equation 2

Hence P (1 + r/100) r = 24 000, now substitute Pr from equation 1

(1 + r/100 ) = 24 000 / 22 500

r /100 = 0.0667

amount after 1 year = Rs 3 600

amount after 2 nd year = Rs 3, 840

15=225XR/100

R=1500/225=6.67%

PR/100=225

PR=22500

P=22500X3/20=3375

So the original sum is 3375