Dividing an Amount in 3 Parts to get Same Simple Interest for 2, 2.5, and 5 Years at 4% p.a.

To divide an amount of 5500 in 3 parts so that the Simple Interest (SI) for all three parts comes the same for 2, 2.5, and 5 years at 4% p.a., we need to follow the below steps:

Step 1: Calculate SI for Each Part for Different Time Periods

We know that the formula for calculating Simple Interest is SI = (P x R x T) / 100, where P is the principal amount, R is the rate of interest, and T is the time period.

Let's calculate SI for each part for different time periods:

- For 2 years: SI = (P x R x T) / 100 = (P x 4 x 2) / 100 = 0.08P
- For 2.5 years: SI = (P x R x T) / 100 = (P x 4 x 2.5) / 100 = 0.1P
- For 5 years: SI = (P x R x T) / 100 = (P x 4 x 5) / 100 = 0.2P

Step 2: Find Three Numbers Whose Ratios are 0.08, 0.1, and 0.2

To divide 5500 in three parts such that the SI for all three parts comes the same for 2, 2.5, and 5 years at 4% p.a., we need to find three numbers whose ratios are 0.08, 0.1, and 0.2.

Let's assume the three numbers as x, y, and z.

So, we have:

- x:y:z = 0.08:0.1:0.2
- x:y:z = 4:5:10 (multiplying by 100)

Step 3: Divide 5500 in Three Parts Using the Ratios

Now, we can divide 5500 in three parts using the ratios obtained in step 2.

Let's assume the three parts as A, B, and C.

So, we have:

- A:B:C = 4:5:10
- A + B + C = 5500

Using the above equations, we can find the values of A, B, and C as follows:

- A = (4 / 19) x 5500 = 1157.89
- B = (5 / 19) x 5500 = 1447.37
- C = (10 / 19) x 5500 = 2894.74

Step 4: Check if SI for Each Part is Same for Different Time Periods

Finally, we need to check if the SI for each part is the same for different time periods.

Let's calculate SI for each part for 2, 2.5, and 5 years:

- For A:
- SI for 2 years = (1157.89 x 4 x 2) / 100 = 92.63
- SI