If the length and the breadth of a rectangle are increased by 15% and 20%, respectively, then by how much percent the area of the rectangle will increase?

38%

Let the length and breadth of the rectangle = 100

According to the questions, 

Length increase 15% = 115,

Breadth increase 20% = 120

Old area = 100 × 100 = 10000

New area = 115 × 120 = 13800

Percentage change = \(\frac{13800 - 10000}{10000 }\) × 100  =  38%