A sum of Rs. 2000 amounts to Rs. 3000 in two years at simple interst. Interest for three years is ______.

Answer

To find the interest for three years on a sum of Rs. 2000 that amounts to Rs. 3000 in two years at simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Amount (P)**:
The principal amount (P) is given as Rs. 2000.

2. **Identify the Amount after 2 Years (A)**:
The amount after 2 years (A) is given as Rs. 3000.

3. **Calculate the Total Interest Earned in 2 Years (SI)**:
The simple interest (SI) for 2 years can be calculated using the formula:
\[ SI = A - P \]
Substituting the values:
\[ SI = 3000 - 2000 = 1000 \text{ Rs.} \]

4. **Calculate the Rate of Interest (R)**:
The simple interest for 2 years is Rs. 1000. To find the rate of interest (R), we can use the formula for simple interest:
\[ SI = \frac{P \times R \times T}{100} \]
Here, T (time) is 2 years. Rearranging the formula to find R:
\[ R = \frac{SI \times 100}{P \times T} \]
Substituting the values:
\[ R = \frac{1000 \times 100}{2000 \times 2} = \frac{100000}{4000} = 25\% \]

5. **Calculate the Interest for 3 Years**:
Now that we have the rate of interest, we can calculate the simple interest for 3 years using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
Here, T is now 3 years. Substituting the values:
\[ SI = \frac{2000 \times 25 \times 3}{100} = \frac{150000}{100} = 1500 \text{ Rs.} \]

### Final Answer:
The interest for three years is **Rs. 1500**.

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