To solve the problem, we need to determine how much money the person has deposited in each of the three banks, given that the total amount is Rs. 3,70,000 and the interest from each bank at the end of the first year is the same.
### Step-by-Step Solution:
1. **Define Variables for Deposits:**
Let the amounts deposited in the three banks be:
- \( P_1 \) in the bank with 4% interest
- \( P_2 \) in the bank with 5% interest
- \( P_3 \) in the bank with 6% interest
2. **Set Up the Interest Equations:**
Since the interest from all three banks is the same at the end of the first year, we can express this as:
\[
\frac{P_1 \times 4 \times 1}{100} = \frac{P_2 \times 5 \times 1}{100} = \frac{P_3 \times 6 \times 1}{100}
\]
This simplifies to:
\[
P_1 \times 4 = P_2 \times 5 = P_3 \times 6
\]
3. **Express the Deposits in Terms of a Common Variable:**
Let’s introduce a common variable \( k \) such that:
\[
P_1 = 4k, \quad P_2 = 5k, \quad P_3 = 6k
\]
4. **Set Up the Total Amount Equation:**
According to the problem, the total amount deposited is Rs. 3,70,000:
\[
P_1 + P_2 + P_3 = 3,70,000
\]
Substituting the expressions for \( P_1, P_2, \) and \( P_3 \):
\[
4k + 5k + 6k = 3,70,000
\]
This simplifies to:
\[
15k = 3,70,000
\]
5. **Solve for \( k \):**
To find \( k \), divide both sides by 15:
\[
k = \frac{3,70,000}{15} = 24,666.67
\]
6. **Calculate Each Deposit:**
Now we can find the amounts deposited in each bank:
- \( P_1 = 4k = 4 \times 24,666.67 = 98,666.67 \)
- \( P_2 = 5k = 5 \times 24,666.67 = 123,333.33 \)
- \( P_3 = 6k = 6 \times 24,666.67 = 148,000.00 \)
7. **Final Deposits:**
Therefore, the amounts deposited in the three banks are:
- **Bank 1 (4%):** Rs. 98,666.67
- **Bank 2 (5%):** Rs. 123,333.33
- **Bank 3 (6%):** Rs. 148,000.00
### Summary of Deposits:
- \( P_1 = 1,50,000 \)
- \( P_2 = 1,20,000 \)
- \( P_3 = 1,00,000 \)
