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

Options

A. 6yr
B. 4yr
C. 3yr
D. None of the above

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI):

**Formula for Simple Interest:**
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest (per annum)
- \( T \) = Time (in years)

### Step 1: Calculate the Simple Interest for the first man
The first man deposited Rs. 9000 at an interest rate of 6% per annum for 4 years.

Using the formula:
\[ \text{SI}_1 = \frac{9000 \times 6 \times 4}{100} \]

Calculating:
\[ \text{SI}_1 = \frac{9000 \times 6 \times 4}{100} = \frac{216000}{100} = 2160 \]

### Step 2: Set up the equation for the second man
Let \( T \) be the time (in years) for which the second man deposits Rs. 5400 at 5% per annum. We want to find \( T \) such that the interest earned by both men is the same.

Using the formula for the second man:
\[ \text{SI}_2 = \frac{5400 \times 5 \times T}{100} \]

### Step 3: Set the interests equal
Since both interests are equal:
\[ 2160 = \frac{5400 \times 5 \times T}{100} \]

### Step 4: Simplify the equation
Multiply both sides by 100 to eliminate the fraction:
\[ 216000 = 5400 \times 5 \times T \]

Calculating \( 5400 \times 5 \):
\[ 5400 \times 5 = 27000 \]

Now the equation is:
\[ 216000 = 27000 \times T \]

### Step 5: Solve for \( T \)
To find \( T \), divide both sides by 27000:
\[ T = \frac{216000}{27000} \]

Calculating:
\[ T = 8 \]

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