If the length of a rectangle is increased by 40%, and the breadth is decreased by 20%. then the area of the rectangle increases by x%. Then the value of x is:

Options

A. 20
B. 12
C. 16
D. 8

Answer

To solve the problem step by step, we need to calculate the percentage change in the area of the rectangle when the length and breadth are changed.

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

### Step 2: Calculate the new dimensions after the changes
- The length is increased by 40%, so the new length \( L' \) is:
\[ L' = L + 0.4L = 1.4L \]
- The breadth is decreased by 20%, so the new breadth \( B' \) is:
\[ B' = B - 0.2B = 0.8B \]

### Step 3: Calculate the original area and the new area
- The original area \( A \) of the rectangle is:
\[ A = L \times B \]
- The new area \( A' \) after the changes is:
\[ A' = L' \times B' = (1.4L) \times (0.8B) = 1.12LB \]

### Step 4: Calculate the change in area
- The change in area can be calculated as:
\[ \text{Change in Area} = A' - A = 1.12LB - LB = (1.12 - 1)LB = 0.12LB \]

### Step 5: Calculate the percentage increase in area
- The percentage increase in area \( x \) is given by:
\[ x = \left( \frac{\text{Change in Area}}{\text{Original Area}} \right) \times 100 = \left( \frac{0.12LB}{LB} \right) \times 100 = 12\% \]

### Conclusion
Thus, the value of \( x \) is 12%.