Malti has deposited certain sum in a bank at `3.5%` per annum. The bank announces an increase in the interest rate by `1.5%` p.a. Malti deposits an additional `₹2500` in the bank. The annual interest that Malti receives now is `₹221`, more than what she would have got earlier. Find the original deposite.

Answer

To find Malti's original deposit, we can follow these steps:

### Step 1: Define the variables
Let the original deposit amount be \( x \).

### Step 2: Calculate the original interest
The original interest rate is \( 3.5\% \) per annum. Therefore, the interest earned on the original deposit in one year is:
\[ \text{Original Interest} = \frac{x \times 3.5 \times 1}{100} = \frac{3.5x}{100} \]

### Step 3: Calculate the new interest rate
The bank increases the interest rate by \( 1.5\% \), making the new interest rate:
\[ \text{New Interest Rate} = 3.5\% + 1.5\% = 5\% \]

### Step 4: Calculate the new interest on the original deposit
The interest earned on the original deposit with the new rate is:
\[ \text{New Interest} = \frac{x \times 5 \times 1}{100} = \frac{5x}{100} \]

### Step 5: Calculate the interest on the additional deposit
Malti deposits an additional \( ₹2500 \). The interest earned on this additional deposit at the new rate is:
\[ \text{Interest on Additional Deposit} = \frac{2500 \times 5 \times 1}{100} = \frac{12500}{100} = 125 \]

### Step 6: Set up the equation
According to the problem, the total interest received now is \( ₹221 \) more than what she would have received earlier. Therefore, we can set up the equation:
\[ \text{New Interest} + \text{Interest on Additional Deposit} = \text{Original Interest} + 221 \]
Substituting the values we calculated:
\[ \frac{5x}{100} + 125 = \frac{3.5x}{100} + 221 \]

### Step 7: Simplify the equation
To eliminate the fractions, multiply the entire equation by \( 100 \):
\[ 5x + 12500 = 3.5x + 22100 \]

### Step 8: Rearranging the equation
Now, rearranging the equation gives:
\[ 5x - 3.5x = 22100 - 12500 \]
\[ 1.5x = 9600 \]

### Step 9: Solve for \( x \)
Now, divide both sides by \( 1.5 \):
\[ x = \frac{9600}{1.5} = 6400 \]

### Step 10: Conclusion
Thus, Malti's original deposit is:
\[ \text{Original Deposit} = ₹6400 \]

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