A sum of Rs 1200 amounts to Rs 1740 in 3 years at simple interest. If rate of interest is increased by 3%, then what will be the new amount (in Rs)?

Options

A. 1848
B. 1946
C. 1812
D. 1924

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Problem
We are given a principal amount (P) of Rs 1200, which amounts to Rs 1740 in 3 years at a certain rate of simple interest. We need to find out the new amount if the rate of interest is increased by 3%.

### Step 2: Calculate the Simple Interest
First, we need to find the simple interest (SI) earned in 3 years. The formula for the amount (A) in simple interest is:
\[ A = P + SI \]
Where:
- \( A \) = Total amount after interest
- \( P \) = Principal amount
- \( SI \) = Simple Interest

From the question:
\[ A = 1740 \]
\[ P = 1200 \]

Now, we can calculate the simple interest:
\[ SI = A - P = 1740 - 1200 = 540 \]

### Step 3: Find the Rate of Interest
We know that:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( R \) = Rate of interest
- \( T \) = Time in years

We can rearrange the formula to find \( R \):
\[ R = \frac{SI \times 100}{P \times T} \]

Substituting the known values:
\[ R = \frac{540 \times 100}{1200 \times 3} \]
\[ R = \frac{54000}{3600} \]
\[ R = 15\% \]

### Step 4: Increase the Rate of Interest
Now, we need to increase the rate of interest by 3%:
\[ \text{New Rate} = R + 3 = 15 + 3 = 18\% \]

### Step 5: Calculate the New Amount
Using the new rate of interest, we will calculate the new amount after 3 years:
\[ A' = P \left(1 + \frac{R' \times T}{100}\right) \]
Where:
- \( R' \) = New Rate of interest

Substituting the values:
\[ A' = 1200 \left(1 + \frac{18 \times 3}{100}\right) \]
\[ A' = 1200 \left(1 + \frac{54}{100}\right) \]
\[ A' = 1200 \left(1 + 0.54\right) \]
\[ A' = 1200 \times 1.54 \]
\[ A' = 1848 \]

### Final Answer
The new amount after increasing the rate of interest by 3% is Rs 1848.

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