Simple interest for three years for a certain sum at the rate of 15% is ₹ 9000. If the rate of interest becomes 30%, then what will be the simple interest for two years?

Options

A. ₹27000
B. ₹4500
C. ₹12000
D. ₹9000

Answer

To solve the problem step by step, we will first find the principal amount (P) using the information given about the simple interest (SI) for 3 years at a rate of 15%. Then we will calculate the simple interest for 2 years at a rate of 30%.

### Step 1: Use the Simple Interest Formula
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

### Step 2: Substitute Known Values to Find P
From the question, we know:
- \( SI = 9000 \)
- \( R = 15\% \)
- \( T = 3 \) years

Substituting these values into the formula:
\[ 9000 = \frac{P \times 15 \times 3}{100} \]

### Step 3: Simplify the Equation
Now, simplify the equation:
\[ 9000 = \frac{45P}{100} \]
\[ 9000 = 0.45P \]

### Step 4: Solve for P
To find \( P \), divide both sides by 0.45:
\[ P = \frac{9000}{0.45} = 20000 \]

### Step 5: Calculate Simple Interest for 2 Years at 30%
Now that we have the principal \( P = 20000 \), we will calculate the simple interest for 2 years at a rate of 30%.

Using the SI formula again:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( R = 30\% \)
- \( T = 2 \) years

Substituting the values:
\[ SI = \frac{20000 \times 30 \times 2}{100} \]

### Step 6: Simplify and Calculate SI
Now simplify:
\[ SI = \frac{20000 \times 60}{100} = \frac{1200000}{100} = 12000 \]

### Final Answer
The simple interest for 2 years at a rate of 30% is ₹ 12000.

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