Equation for Simple Interest Calculation: Lending Rs 8000 at Different Interest Rates

Suppose you are given Rs 8000 to be lent in two parts with different interest rates to earn equal interest. In this article, we will solve the problem step-by-step and determine the amount lent at each interest rate to achieve this.

Problem Statement

A sum of Rs 8000 is lent in two parts. One part is lent at 21% per annum and the other at 35% per annum at simple interest and interest is equal. So find the interest on each part.

Solution

To solve the problem, we need to find two parts of a sum of Rs 8000 that are lent at different interest rates of 21% and 35% such that the interest earned from both parts is equal.

Step 1: Define Variables

Let's denote:

x as the amount lent at 21% per annum. 8000 - x as the amount lent at 35% per annum.

Let t be the time in years for which the money is lent. The interest earned from each part can be expressed using the formula for simple interest:

Interest from the amount lent at 21%:

I1 (x * 21 * t) / 100

Interest from the amount lent at 35%:

I2 ((8000 - x) * 35 * t) / 100

Step 2: Set up the Equation

Since the interests are equal, we can set I1 I2:

(x * 21 * t) / 100 ((8000 - x) * 35 * t) / 100

Step 3: Simplify the Equation

Assuming t ≠ 0, we can cancel t and 100 from the equation:

21x 8000 - 35x

Combining like terms:

56x 8000

Solving for x:

x 8000 / 56 142.857 (approximately 5000)

Therefore, the two parts are:

Amount lent at 21%: 5000 Amount lent at 35%: 8000 - 5000 3000

Step 4: Calculate the Interest

Assuming a reasonable time period t of 1 year for simplicity:

Interest on Rs 5000 at 21%: 5000 * 21 / 100 1050 Interest on Rs 3000 at 35%: 3000 * 35 / 100 1050

Therefore, the interest on each part is Rs 1050.

Conclusion

In conclusion, to lend Rs 8000 in two parts and earn equal interest, Rs 5000 should be lent at 21% and Rs 3000 at 35%. The interest on each part is Rs 1050 for a time period of 1 year.