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 ₹ 480

• A. ₹ 55,000
• B. ₹ 75,000
• C. ₹ 85,000
• D. ₹ 80,000

Answer 1

The correct option is B

₹ 75,000

Let the Principal be $P$

Given C.I - S.I = ₹ 480 , 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 ₹ 480

Hence from (1) and (2) , we have $\frac{1664P}{10000}$ - $\frac{16P}{100}$ = ₹ 480

$\frac{64P}{10000}$ = ₹ 480

P = ₹ 75,000