Question

The original length of a rectangular sports ground was 100 meter and breadth 25 meters. After carrying out some alignment changes, the length becomes 50 meter and breadth becomes 75 meters. What is the percentage change in area?

• A. 20 %
• B. 30 %
• C. 50 %
• D. 100 %

Hint:

For percentage change problems involving multiplication (like Area = L \(\times\) B), you can use the successive percentage change formula: \( A + B + \frac{AB}{100} \). Here, Length change (A) = \(\frac{50-100}{100} = -50%\). Breadth change (B) = \(\frac{75-25}{25} = +200%\). Change = \( -50 + 200 + \frac{(-50)(200)}{100} = 150 - \frac{10000}{100} = 150 - 100 = +50%\). This method can be faster if the numbers are simple.

Answer 1

The Correct Option is C

Step 1: Understanding the Problem
We need to calculate the percentage change in the area of a rectangle after its length and breadth are changed.

Step 2: Key Formula or Approach
\begin{enumerate}
Calculate the original area.
Calculate the new area.
Calculate the change in area.
Calculate the percentage change using the formula: \[ \text{Percentage Change} = \frac{\text{Change in Area}}{\text{Original Area}} \times 100% \] \end{enumerate}
Step 3: Detailed Explanation
1. Calculate the Original Area:
Original Length (\(L_1\)) = 100 m
Original Breadth (\(B_1\)) = 25 m
\[ \text{Original Area} (A_1) = L_1 \times B_1 = 100 \times 25 = 2500 \text{ sqm} \] 2. Calculate the New Area:
New Length (\(L_2\)) = 50 m
New Breadth (\(B_2\)) = 75 m
\[ \text{New Area} (A_2) = L_2 \times B_2 = 50 \times 75 = 3750 \text{ sqm} \] 3. Calculate the Change in Area:
\[ \text{Change in Area} = A_2 - A_1 = 3750 - 2500 = 1250 \text{ sqm} \] Since the new area is larger, this is an increase.
4. Calculate the Percentage Change:
\[ \text{Percentage Change} = \frac{\text{Change in Area}}{\text{Original Area}} \times 100% \] \[ \text{Percentage Change} = \frac{1250}{2500} \times 100% \] \[ \text{Percentage Change} = \frac{1}{2} \times 100% = 50% \] The area has increased by 50%.

Step 4: Final Answer
The percentage change in the area is a 50% increase. Therefore, option (C) is the correct answer.