Puri had invested a certain sum of money in a bank at `4.5%` per annum. The bank reduced the rate of interest by `0.5%` p.a. Puri withdrew `₹4,000` from his account. At the end of the year, the interest he got was `₹200` less than what he would have got had the bank not reduced the interest rate and he had not withdrew `₹4000`. Find the original deposite.

Answer

To solve the problem step by step, let's break down the information provided and use the formula for simple interest.

### Step 1: Define the Variables
Let the original deposit be represented as \( P \). According to the problem, the interest rate was initially \( 4.5\% \) per annum but was reduced by \( 0.5\% \). Therefore, the new interest rate is:
\[ R = 4.5\% - 0.5\% = 4\% \]

### Step 2: Calculate the Interest Without Withdrawal
If Puri had not withdrawn any money, the interest he would have received at the original rate for one year would be:
\[ \text{Interest} = \frac{P \times R \times T}{100} = \frac{P \times 4.5 \times 1}{100} = \frac{4.5P}{100} \]

### Step 3: Calculate the Interest After Withdrawal
Puri withdrew \( ₹4000 \), so the remaining amount in his account is:
\[ \text{Remaining Amount} = P - 4000 \]
The interest on this remaining amount at the new rate of \( 4\% \) for one year would be:
\[ \text{Interest after withdrawal} = \frac{(P - 4000) \times 4 \times 1}{100} = \frac{4(P - 4000)}{100} = \frac{4P - 16000}{100} \]

### Step 4: Set Up the Equation
According to the problem, the interest he received after the withdrawal was \( ₹200 \) less than what he would have received if he had not withdrawn the money. Therefore, we can set up the equation:
\[ \frac{4.5P}{100} - 200 = \frac{4P - 16000}{100} \]

### Step 5: Eliminate the Denominator
To eliminate the denominator, multiply the entire equation by \( 100 \):
\[ 4.5P - 20000 = 4P - 16000 \]

### Step 6: Rearrange the Equation
Rearranging the equation gives:
\[ 4.5P - 4P = 20000 - 16000 \]
\[ 0.5P = 4000 \]

### Step 7: Solve for \( P \)
Now, divide both sides by \( 0.5 \):
\[ P = \frac{4000}{0.5} = 8000 \]

### Conclusion
Thus, the original deposit that Puri made is:
\[ \text{Original Deposit} = ₹8000 \]