In what time will Rs 72 become Rs 81 to `6 (1)/(4) %` per annum simple interest?

Options

A. 2 years
B. 3 years
C. 2 years 6 months
D. None of these

Answer

To solve the problem of how long it will take for Rs 72 to become Rs 81 at a simple interest rate of 6.25% per annum, we can follow these steps:

### Step 1: Identify the principal, amount, and rate of interest
- **Principal (P)** = Rs 72
- **Amount (A)** = Rs 81
- **Rate of Interest (R)** = 6.25% per annum

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = A - P \]
Substituting the values:
\[ \text{SI} = 81 - 72 = Rs 9 \]

### Step 3: Convert the rate of interest from percentage to decimal
To use the formula for simple interest, we need to convert the percentage into a decimal:
\[ R = 6.25\% = \frac{6.25}{100} = 0.0625 \]

### Step 4: Use the Simple Interest formula to find time (T)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Rearranging the formula to find time (T):
\[ T = \frac{\text{SI} \times 100}{P \times R} \]
Substituting the known values:
\[ T = \frac{9 \times 100}{72 \times 6.25} \]

### Step 5: Calculate the denominator
First, calculate \( 72 \times 6.25 \):
\[ 72 \times 6.25 = 450 \]

### Step 6: Substitute back into the time formula
Now substitute back into the time formula:
\[ T = \frac{900}{450} \]

### Step 7: Simplify to find T
\[ T = 2 \text{ years} \]

### Final Answer
The time required for Rs 72 to become Rs 81 at a simple interest rate of 6.25% per annum is **2 years**.

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