If rectangles lengths increase `20%` and breadth decrease `16(2)/(3)%` then what will be effect in area of rectangle ?

Options

A. a) `20%` increase
B. b) `30%` increase
C. c) `10%` decrease
D. d) No change

Answer

To determine the effect on the area of a rectangle when its length increases by 20% and its breadth decreases by \(16 \frac{2}{3}\%\), we can follow these steps:

### Step 1: Understand the Problem
We know that the area \(A\) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
We need to find out how the area changes when the length increases by 20% and the breadth decreases by \(16 \frac{2}{3}\%\).

### Step 2: Convert Percentages to Decimal
- The increase in length is \(20\%\), which can be converted to decimal as:
\[ \text{Increase in Length} = \frac{20}{100} = 0.20 \]
- The decrease in breadth is \(16 \frac{2}{3}\%\). First, convert \(16 \frac{2}{3}\%\) to an improper fraction:
\[ 16 \frac{2}{3} = \frac{50}{3}\% \]
Now, convert this percentage to decimal:
\[ \text{Decrease in Breadth} = \frac{50}{3 \times 100} = \frac{50}{300} = \frac{1}{6} \approx 0.1667 \]

### Step 3: Calculate New Length and Breadth
Let the original length be \(L\) and the original breadth be \(B\).
- New Length after a 20% increase:
\[ \text{New Length} = L + 0.20L = 1.20L \]
- New Breadth after a \(16 \frac{2}{3}\%\) decrease:
\[ \text{New Breadth} = B - \frac{1}{6}B = \frac{5}{6}B \]

### Step 4: Calculate New Area
Now, we can calculate the new area using the new dimensions:
\[ \text{New Area} = \text{New Length} \times \text{New Breadth} = (1.20L) \times \left(\frac{5}{6}B\right) \]
\[ \text{New Area} = 1.20 \times \frac{5}{6} \times L \times B \]
\[ \text{New Area} = 1.20 \times \frac{5}{6} \times A \]
Where \(A\) is the original area \(L \times B\).

### Step 5: Simplify the New Area
Now, simplify \(1.20 \times \frac{5}{6}\):
\[ 1.20 = \frac{12}{10} = \frac{6}{5} \]
\[ \text{New Area} = \frac{6}{5} \times \frac{5}{6} \times A = A \]

### Conclusion
The new area is equal to the original area, which means there is no change in the area of the rectangle.

### Final Answer
The effect on the area of the rectangle is that there is **no change**.

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