Question

A property is bought for Rs.75450. It is expected that the value of the property will appreciate 25% in two years. The value of the property at the end of two years will be

• A. Rs .94312.50
• B. Rs. 94322.50
• C. Rs. 93312.50
• D. Rs. 94302.50

Hint:

To easily find \(125\%\) of any number, calculate the number itself plus one-quarter of its value:
\(75450 + (75450 \div 4) = 75450 + 18862.5 = 94312.5\).
This mental math approach saves significant time during exams.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This is a commercial mathematics question dealing with percentage increase (appreciation) of a given value over a specified time frame.

Step 2: Key Formulas and approach:
The initial value (purchase price) of the property is given as \(\text{Rs. } 75,450\).
The property is expected to appreciate by \(25\%\) over the course of two years.
The wording "will appreciate 25% in two years" indicates that the total growth over the two-year period is a flat \(25\%\) of the original purchase price.
The formula to calculate the final appreciated value is:
\[ \text{Appreciated Value} = \text{Original Value} \times \left(1 + \frac{\text{Appreciation Rate}}{100}\right) \]

Step 3: Detailed Explanation:

• Let the initial purchase price be \(P = \text{Rs. } 75,450\).

• The total appreciation percentage is \(R = 25\%\).

• Substitute the values into the formula:
\[ \text{Appreciated Value} = 75450 \times \left(1 + \frac{25}{100}\right) \] \[ \text{Appreciated Value} = 75450 \times 1.25 \]

• Let us perform the multiplication step-by-step:
\[ 75450 \times 1.25 = 75450 \times \left(\frac{5}{4}\right) \] \[ \frac{75450 \times 5}{4} = \frac{377250}{4} \] \[ \frac{377250}{4} = 94312.50 \]

• The value of the property at the end of two years is therefore \(\text{Rs. } 94,312.50\).


Step 4: Final Answer:
The correct final value of the property is \(\text{Rs. } 94,312.50\), which is Option (A).