If the simple interest on certain sum of money be Rs. 40

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If the simple interest on certain sum of money be Rs. 40 for 2 years and the compound interest on the same sum at the same rate and for the same time be Rs. 45. What is the principle ?

1. Rs. 70
2. Rs. 90
3. Rs. 85
4. Rs. 80

Correct Option: D

S.I. for 2 year = Rs. 40
S.I. for 1 year = Rs. 20
Rate = {(C.I. for 2 year - S.I. for 2 year) / (S.I. for 1 year)} x 100
= {(45 - 40) / 20} x 100 = 25%

∴ Principal = (S.I. x 100)/(Rate x Time)
= (40 x 100)/(25 x 2)
= Rs. 80