A man deposits a certain amount in a bank at 7% per annum simple interest. If he had deposited the same money in a post office, he could get 8.5% per annum and in that case he would have received ₹300 more. How much money had he deposited in the bank?

Questions : A man deposits a certain amount in a bank at 7% per annum simple interest. If he had deposited the same money in a post office, he could get 8.5% per annum and in that case he would have received ₹300 more. How much money had he deposited in the bank?

Answer:  

 The formula for Simple Interest (SI) is:

$$SI = \frac{P \times R \times T}{100}$$

Let the deposited amount be P and the time period be T years (same for both bank and post office).
Given:

• Bank interest rate = 7% per annum
• Post office interest rate = 8.5% per annum
• The additional interest from the post office = ₹300

Step 1: Find the interest difference equation

$$\left(\frac{P \times 8.5 \times T}{100}\right) - \left(\frac{P \times 7 \times T}{100}\right) = 300$$

Factor out P × T / 100:

$$P \times T \times \frac{(8.5 - 7)}{100} = 300$$ $$P \times T \times \frac{1.5}{100} = 300$$ $$P \times T = \frac{300 \times 100}{1.5}$$ $$P \times T = 20000$$

Step 2: Find P

Since the time period T is not given, we assume it remains T years.
Thus, the deposited amount P depends on the time period.
If T = 1 year, then:

$$P = 20000$$

So, the deposited amount in the bank is ₹20,000 for 1 year. If the time period differs, the deposited amount will change proportionally.

Additional Techniques 

Here's how to solve this problem:

1. Understand the Problem

The difference in interest rates between the bank and the post office is what accounts for the extra ₹300. We need to find the principal amount that would generate this difference.

2. Calculate the Difference in Interest Rates

• Post office rate: 8.5%
• Bank rate: 7%
• Difference: 8.5% - 7% = 1.5%

3. Relate the Interest Difference to the Principal

The 1.5% difference in interest rates on the principal amount is equal to the ₹300 extra he would have received.

4. Calculate the Principal

Let 'P' be the principal amount.

1.5% of P = ₹300

(1.5/100) * P = 300

P = (300 * 100) / 1.5

P = 20000

Answer: The man deposited ₹20,000 in the bank.

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