Question

The difference between CI and SI for 2 years on the same sum at 5% p.a. is ₹ 240. Find the sum.

Answer 1

Given, the difference between CI and SI for 2 years on the same sum at 5% per annum is ₹ 240.

Let the given sum be ₹ P.

Simple interest = `(PRT)/100`, where P is the principal, R is the rate of interest and T is the time period

Compound interest = `P[(1 + R/100)^T - 1]`, where P is the principal, R is the rate of interest and T is the time period

∴ `P[(1 + 5/100)^2 - 1] - (P xx 5 xx 2)/100 = 240`

⇒ `P[(1 + 1/20)^2 - 1] - P/10 = 240`

⇒ `P[(21/20)^2 - 1] - P/10 = 240`

⇒ `P[441/400 - 1] - P/10 = 240`

⇒ `P[(441 - 400)/400] - P/10 = 240`

⇒ `(41P)/400 - P/10 = 240`

⇒ `(41P - 40P)/400 = 240`

⇒ `P = 240 xx 400`

⇒ `P = 96000`

Hence, the required sum is ₹ 96000.