If the length of a rectangle is increased by 37 ½ % and its breadth is decreased by 20% . Then find the percentage change in its area ?

Sure, here are the steps to solve this problem:

1. Let's assume the original length of the rectangle is 100 units and the original breadth is also 100 units. So, the original area of the rectangle is 100*100 = 10,000 square units.

2. According to the problem, the length of the rectangle is increased by 37 ½ %. So, the new length is 100 + 37.5 = 137.5 units.

3. The breadth of the rectangle is decreased by 20%. So, the new breadth is 100 - 20 = 80 units.

4. Now, the new area of the rectangle is 137.5*80 = 11,000 square units.

5. The change in the area is 11,000 - 10,000 = 1,000 square units.

6. To find the percentage change in the area, we divide the change in the area by the original area and then multiply by 100. So, the percentage change in the area is (1,000/10,000)*100 = 10%.

So, the percentage change in the area of the rectangle is 10%.