Question

The difference between simple interest and compound interest on a certain sum is ₹54.40 for 2 years at 8 per cent per annum. Find the sum.

• A. ₹8,300
• B. ₹8,500
• C. ₹8,400
• D. ₹8,600

Answer 1

Answer: (B)

Let’s assume the principal (P) = x

R = 8%

T = 2 years

Now,

The simple interest is calculated as

S.I. $=\frac{PRT}{100}$

S.I. $=\frac{(x\times 8\times 2)}{100}$

$=\frac{4x}{25}$

The compound interest is calculated as

C.I. = A – P

= x(1 + $\frac{8}{100}$)² – x)

= x[(1 + $\frac{2}{25}$)² – 1]

= x[($\frac{27}{25}$)²- 1]

= $\frac{104x}{625}$

Given, C.I. - S.I. = 54.40

$\frac{104x}{625}$ – $\frac{4x}{25}$ = 54.40

x ( $\frac{104}{625}$– $\frac{4}{25}$) = 54.40

x ($\frac{104}{625}$ – $\frac{100}{625}$) = 54.40

x ($\frac{4}{625}$) = 54.40

x =$\frac{\left(54.40x625\right)}{4}$

x = 8500

Thus, the principal sum is ₹8,500