A man deposited ₹ 9000 in a bank at 6% per annum for 4 yr. For how many years, must another man deposit an amount of ₹ 5400 at 5% per annum in another bank so that. Both of them get the same interest?

Options

A. 6 yr
B. 4 yr
C. 3 yr
D. none of these

Answer

To solve the problem step by step, we will calculate the simple interest earned by the first man and then determine how long the second man needs to deposit his amount to earn the same interest.

### Step 1: Calculate the Simple Interest for the First Man
The formula for Simple Interest (SI) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

For the first man:
- Principal (\( P \)) = ₹ 9000
- Rate (\( R \)) = 6%
- Time (\( T \)) = 4 years

Substituting the values into the formula:
\[ \text{SI} = \frac{9000 \times 6 \times 4}{100} \]

### Step 2: Calculate the Interest
Calculating the above expression:
\[ \text{SI} = \frac{9000 \times 6 \times 4}{100} = \frac{216000}{100} = ₹ 2160 \]

### Step 3: Set Up the Equation for the Second Man
Now, we need to find out for how many years (\( T_2 \)) the second man must deposit ₹ 5400 at 5% per annum to earn the same interest of ₹ 2160.

Using the same formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T_2}{100} \]
Substituting the values for the second man:
- Principal (\( P \)) = ₹ 5400
- Rate (\( R \)) = 5%
- Interest (\( \text{SI} \)) = ₹ 2160

So we have:
\[ 2160 = \frac{5400 \times 5 \times T_2}{100} \]

### Step 4: Solve for \( T_2 \)
Rearranging the equation to solve for \( T_2 \):
\[ 2160 = \frac{5400 \times 5 \times T_2}{100} \]
Multiplying both sides by 100:
\[ 216000 = 5400 \times 5 \times T_2 \]
\[ 216000 = 27000 \times T_2 \]
Now, divide both sides by 27000:
\[ T_2 = \frac{216000}{27000} \]
Calculating \( T_2 \):
\[ T_2 = 8 \]

### Conclusion
The second man must deposit the amount for **8 years** to earn the same interest as the first man.