Question

Find the sum invested if the difference between S.I. and C.I. on a sum for 2 years at $8\%$ per annum is ₹160.

• A. ₹25,000
• B. ₹25,500
• C. ₹25,400
• D. ₹26,000

Answer 1

The correct option is A

₹25,000

Let the principal be $P$.

Given C.I. - S.I. = ₹160, n = 2 years and r = 8%

S.I. = $\frac{P\times T\times R}{100}$

= $\frac{P\times 2\times 8}{100}$

= $\frac{16P}{100}$ -----(1)

C.I for the first year = $\frac{P\times 1\times 8}{100}$

= $\frac{8P}{100}$

Principal for 2nd year = P + $\frac{8P}{100}$ = $\frac{108P}{100}$

C.I. for the second year = $\frac{108P\times 1\times 8}{100\times 100}$

= $\frac{864P}{10000}$

Total C.I. for two years = $\frac{864P}{10000}$ + $\frac{8P}{100}$

= $\frac{1664P}{10000}$ -----(2)

Given that the difference between C.I. and S.I. is ₹160.

Hence from (1) and (2) , we have

$\frac{1664P}{10000}$ - $\frac{16P}{100}$ = ₹160

$\frac{64P}{10000}$ = ₹160

$P$ = ₹25,000