The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by ₹ 82. Find the sum.

Let the required sum be ₹ P.

Simple interest for 3 years

= (P×R×T)/100 = (P× 5 × 3)/100 = Rs 3P/20

Simple interest for 4 years = (P × R × T)/100

= (P × 5 × 4)/100 = Rs 4P/20

As per the question, we have

4P/20 – 3P/20 = 82 ⇒ P/20 = 82

⇒ P = 20 × 82 = Rs 1640

Hence, the required sum = Rs 1640

Alternate Method

Simple Interest gained from 3rd to 4th year = ₹ 82

Time (4th year – 3rd year) = 1 year

P =  (SI×100)/(R×T)

P =  (82×100)/(5×1)=1640

Required sum = ₹ 1640