# The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 1. The sum (in Rs.) is:

A. 625

B. 630

C. 640

D. 650

E. None of these

**Answer: Option A **

__Solution(By Examveda Team)__

$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{sum}}\,{\text{be}}\,Rs.\,x.\,{\text{Then}}, \cr
& {\text{C}}{\text{.I}}{\text{.}} = {x{{\left( {1 + \frac{4}{{100}}} \right)}^2} - x} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\frac{{676}}{{625}}x - x} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{51}}{{625}}x \cr
& {\text{S}}{\text{.I}}{\text{.}} = {\frac{{x \times 4 \times 2}}{{100}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2x}}{{25}} \cr
& \therefore \frac{{51x}}{{625}} - \frac{{2x}}{{25}} = 1 \cr
& \Rightarrow x = 625 \cr} $$ ## Join The Discussion

## Comments ( 6 )

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4×4/100×100=1

25*25=625

Use PR^2/10^4

Why x is subtracted frm CI

Why -x is used

And hay 51/625 calculate

Haw 676 calculate plz