Sum of rupees 25000 amount to rupees 40000 in 8 years at certain rate of interest what will be the simple interest on on the same sum for 7 year at double the interstate

The problem is based on simple interest (SI). Let's first break it down and solve it step-by-step.

### Step 1: Finding the Rate of Interest
We know that the principal (P) is ₹25,000, the amount (A) is ₹40,000, and the time (T) is 8 years. We use the formula for the amount in simple interest:

\[
A = P + SI
\]

where:
- \(A = 40,000\) (final amount)
- \(P = 25,000\) (initial principal)
- \(SI\) is the simple interest

First, calculate the simple interest \(SI\) for 8 years:

\[
SI = A - P = 40,000 - 25,000 = 15,000
\]

Now, use the formula for simple interest to find the rate of interest (\(R\)):

\[
SI = \frac{P \times R \times T}{100}
\]

Substitute the known values:

\[
15,000 = \frac{25,000 \times R \times 8}{100}
\]

Simplifying:

\[
15,000 = 2,000R
\]

\[
R = \frac{15,000}{2,000} = 7.5\%
\]

So, the rate of interest is 7.5%.

### Step 2: Calculating Simple Interest for 7 Years at Double the Rate
The problem now asks for the simple interest on ₹25,000 for 7 years at double the rate of interest. The rate is doubled from 7.5% to \(2 \times 7.5 = 15\%\).

Now, use the simple interest formula again:

\[
SI = \frac{P \times R \times T}{100}
\]

Substitute the values:

\[
SI = \frac{25,000 \times 15 \times 7}{100}
\]

Simplify:

\[
SI = \frac{25,000 \times 105}{100} = 26,250
\]

### Conclusion:
The simple interest on ₹25,000 for 7 years at double the rate of interest (15%) is ₹26,250.

---

Would you like more details on any part of this? Here are 5 related questions:

1. How does compound interest differ from simple interest in such problems?
2. What would be the total amount after 7 years at this new rate?
3. How would the calculation change if the interest were compounded annually?
4. What happens to the simple interest if the time is halved and the rate remains constant?
5. How would you calculate the interest if it were compounded semi-annually?

**Tip:** In simple interest problems, the interest is directly proportional to both the time and the rate, making calculations straightforward.

Sum of rupees 25000 amount to rupees 40000 in 8 years at certain rate of interest what will be the simple interest on the same sum for 7 years at double the interest rate?

Learn how to calculate the simple interest on ₹25,000 over 7 years at double the interest rate. Starting with a principal of ₹25,000, we find the interest rate and calculate the final simple interest of ₹26,250. Suitable for students in Grades 8-10.

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