Question

Divide Rs. 15,600 into two parts such that the interest on one at 5 percent for 5 years may be equal to that on the other at `4 1/2` percent for 6 years.

Answer 1

Given:

1. Total amount = Rs. 15,600,
2. Interest rates:
   • First part: 5% for 5 years,
   • Second part: 4.5% for 6 years,
3. The interest on both parts is equal.

Step 1: Set up the equation for equal interest

Let the first part be x and the second part be 15,600 − x.

The formula for simple interest is:

`Interest = (PxxRxxT)/100`

For the first part: 

Interest on first part = `(x xx5 xx5)/100`

For the second part:

Interest on second part = `((15600-x) xx4.5xx6)/100`

Equating the two:

`(x xx 5xx5)/100 = ((15600-x)xx4.5xx6)/100`

Step 2: Solve for x

Simplify the equation:

25x = 27 × (15,600 − x).

25x = 421200 − 27x.

25x + 27x = 421200.

52x = 421200.

`x=421200/52 = 8100`

Step 3: Calculate the second part

15600 − x = 15,600 − 8,100 = 7,500.

• First part: Rs. 8,100,
• Second part: Rs. 7,500.