A sum of Rs.4,000 becomes Rs.8,000 in 10 years. At what % rate the simple interest is
calculated?
(A) 12.5% (B) 15% (C) 5% (D) 10%

To solve for the rate of simple interest, we can use the formula for simple interest:

\[
A = P(1 + \frac{r \cdot t}{100})
\]

Where:
- \( A \) is the total amount after interest (Rs. 8,000)
- \( P \) is the principal amount (Rs. 4,000)
- \( r \) is the rate of interest (what we need to find)
- \( t \) is the time in years (10 years)

Substituting the given values into the formula:

\[
8,000 = 4,000(1 + \frac{r \cdot 10}{100})
\]

Dividing both sides by 4,000:

\[
2 = 1 + \frac{r \cdot 10}{100}
\]

Subtract 1 from both sides:

\[
1 = \frac{r \cdot 10}{100}
\]

Now, solve for \( r \):

\[
r \cdot 10 = 100
\]

\[
r = \frac{100}{10} = 10
\]

So, the rate of interest is **10%**.

Thus, the correct answer is **(D) 10%**.

Would you like more details on this or have any other questions?

Here are 5 related questions for practice:
1. If Rs. 6,000 becomes Rs. 9,000 in 5 years, what is the simple interest rate?
2. How long will it take for Rs. 5,000 to double at a rate of 8% simple interest?
3. What will be the total amount for a Rs. 3,000 loan at 12% simple interest after 7 years?
4. If Rs. 2,500 becomes Rs. 4,500 in 15 years, what is the rate of simple interest?
5. How much interest is earned on Rs. 10,000 at 6% simple interest over 3 years?

**Tip**: Simple interest grows linearly with time, so doubling the principal with a constant rate means doubling the time needed.

A sum of Rs.4,000 becomes Rs.8,000 in 10 years. At what % rate the simple interest is calculated? (A) 12.5% (B) 15% (C) 5% (D) 10%

Discover how to calculate the simple interest rate that doubles a Rs.4,000 sum to Rs.8,000 in 10 years. This example uses the formula A = P(1 + rt/100), teaching key algebraic concepts and interest calculations for students in Grades 8-10.

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