If the length of a rectangle is decreased by 20% and breadth is decreased by 40%, then what will be the percentage decrease in the area of the rectangle ?

Options

A. 48
B. 52
C. 60
D. 40

Answer

To find the percentage decrease in the area of a rectangle when the length is decreased by 20% and the breadth is decreased by 40%, we can follow these steps:

### Step 1: Define the original dimensions of the rectangle
Let the original length of the rectangle be \( L = 10x \) and the original breadth be \( B = 10y \).

### Step 2: Calculate the new dimensions after decrease
- The length is decreased by 20%. Therefore, the new length \( L' \) is:
\[ L' = L - 0.2L = 10x - 0.2(10x) = 10x(1 - 0.2) = 10x \times 0.8 = 8x \]

- The breadth is decreased by 40%. Therefore, the new breadth \( B' \) is:
\[ B' = B - 0.4B = 10y - 0.4(10y) = 10y(1 - 0.4) = 10y \times 0.6 = 6y \]

### Step 3: Calculate the original area of the rectangle
The original area \( A \) of the rectangle is given by:
\[ A = L \times B = (10x) \times (10y) = 100xy \]

### Step 4: Calculate the new area of the rectangle
The new area \( A' \) of the rectangle is given by:
\[ A' = L' \times B' = (8x) \times (6y) = 48xy \]

### Step 5: Calculate the decrease in area
The decrease in area is:
\[ \text{Decrease} = A - A' = 100xy - 48xy = 52xy \]

### Step 6: Calculate the percentage decrease in area
The percentage decrease in area is calculated as:
\[ \text{Percentage Decrease} = \left(\frac{\text{Decrease}}{\text{Original Area}}\right) \times 100 = \left(\frac{52xy}{100xy}\right) \times 100 \]
\[ = 52\% \]

Thus, the percentage decrease in the area of the rectangle is **52%**.