In simple interest, what sum amounts to Rs. 1088 in 6 years and Rs. 1184 in 8…

Concept:

In Simple Interest, the interest earned each year is constant, so the amount grows by the same fixed sum every year. This means the difference between the amounts at two different years equals the interest for exactly the number of years between them.

Application:

1. The difference between the amount at 8 years (Rs. 1184) and at 6 years (Rs. 1088) is Rs. 1184 - Rs. 1088 = Rs. 96, which is the interest earned over the 2 years between them.

2. So the interest earned in one year is Rs. 96 / 2 = Rs. 48.

3. The total interest accumulated over the first 6 years is Rs. 48 x 6 = Rs. 288.

4. The principal is the amount at 6 years minus this accumulated interest: Rs. 1088 - Rs. 288 = Rs. 800.

Cross-check:

Checking: with principal Rs. 800 and yearly interest Rs. 48, the rate is (48/800) x 100 = 6% per annum. At 8 years, the amount would be Rs. 800 + 8 x Rs. 48 = Rs. 800 + Rs. 384 = Rs. 1184, which matches the given data, confirming the principal of Rs. 800.