In what time, Rs.1200 will become Rs.1450 when annual rate of interest is 20%?

Options

A. 1 Yr
B. `1(1)/(13)yr`
C. `1(1)/(24)yr`
D. `1(1)/(20)yr`

Answer

To solve the problem of determining how long it will take for Rs. 1200 to grow to Rs. 1450 at an annual interest rate of 20%, we can follow these steps:

### Step 1: Identify the given data
- Principal (P) = Rs. 1200
- Amount (A) = Rs. 1450
- Rate of Interest (R) = 20%

### Step 2: Calculate the Simple Interest (SI)
Simple Interest can be calculated using the formula:
\[ \text{SI} = \text{Amount} - \text{Principal} \]
Substituting the values:
\[ \text{SI} = 1450 - 1200 = 250 \text{ Rs.} \]

### Step 3: Use the formula for Simple Interest to find Time (T)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
We need to rearrange this formula to solve for time (T):
\[ T = \frac{\text{SI} \times 100}{P \times R} \]

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ T = \frac{250 \times 100}{1200 \times 20} \]

### Step 5: Simplify the expression
Calculating the denominator:
\[ 1200 \times 20 = 24000 \]
Now substituting this back into the equation:
\[ T = \frac{25000}{24000} \]

### Step 6: Simplify the fraction
We can simplify \( \frac{25000}{24000} \):
\[ T = \frac{25}{24} \]

### Step 7: Convert to mixed number
This can be expressed as:
\[ T = 1 \frac{1}{24} \text{ years} \]

### Final Answer
Thus, the time it will take for Rs. 1200 to become Rs. 1450 at an annual interest rate of 20% is \( 1 \frac{1}{24} \) years.

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