If the length of a rectangle is increased by 50%, and the breadth is decreased by 30%, then the area of the rectangle increases by x%. Then the value of x is:

Options

A. A.5
B. B.8
C. C.12
D. D.20

Answer

To find the percentage increase in the area of a rectangle when the length is increased by 50% and the breadth is decreased by 30%, we can follow these steps:

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

### Step 2: Calculate the original area
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

### Step 3: Calculate the new dimensions
- The new length after a 50% increase is:
\[ \text{New Length} = L + 0.5L = 1.5L \]
- The new breadth after a 30% decrease is:
\[ \text{New Breadth} = B - 0.3B = 0.7B \]

### Step 4: Calculate the new area
The new area \( A' \) of the rectangle is given by:
\[ A' = \text{New Length} \times \text{New Breadth} = (1.5L) \times (0.7B) = 1.05LB \]

### Step 5: Calculate the percentage increase in area
To find the percentage increase in area, we can use the formula:
\[ \text{Percentage Increase} = \left( \frac{A' - A}{A} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{1.05LB - LB}{LB} \right) \times 100 \]
\[ = \left( \frac{0.05LB}{LB} \right) \times 100 = 5\% \]

### Conclusion
Thus, the value of \( x \) is \( 5 \).

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