Question

The difference between the compound interest and simple interest on a certain sum for 3 years at 5% p.a. is rs.183. Find the sum.

Answer 1

Your answer

Given,

Time = 3 years

Rate = 5% p. a.

Let the sum be ₹ P.

$si = \frac{p \times r \times t}{100} \\ \\ \: \: \: \: \: = \frac{p \times 5 \times 3}{100} \\ \\ \: \: \: \: \: = \frac{3p}{20}$
CI = { p × ( 1 + r / 100 )^t – p }

= { p × ( 1 + 5 / 100 )^3 – p }

= { p × ( 1 / 20 )^3 – p }

= ( p × 21/20 × 21/20 × 21/20 – p)


$= \frac{9261p}{8000} - p \\ \\ = \frac{9261p - 8000p}{8000} \\ \\ = \frac{1261p}{8000}$

According to question,

CI – SI = 183

$\frac{1261p}{8000} - \frac{3p}{20} = 183 \\ \\ \frac{1261p - 1200p}{8000} = 183 \\ \\ \frac{61p}{8000} = 183 \\ \\ 61p = 183 \times 8000 \\ \\ p = \frac{183 \times 8000}{61} \\ \\ p = 24000$
Hence, the sum is ₹ 24000

Hope it help you