Tips & Tricks
GIVEN: Length of a rectangle is increased by 10% and its breadth is decreased by 20%
.
FORMULA USED: Area of rectangle = Length × Breadth
CALCULATION: Suppose the length and breadth of the rectangle are ‘l’ and ‘b’ respectively.
So, area of rectangle = lb
Now,
Increased length = 1.1l and decreased breadth = 0.8b
⇒ New area = 1.1l × 0.8b = 0.88lb
Decrement in area = [lb – 0.88lb] = 0.12lb
∴ Percentage decrement in area = [0.12lb/lb] × 100
Smart trick Formula for successive percentage change of a% and b% = (a + b + ab/100)
∴ Percentage change in area = 10 – 20 – (200/100) = -12% (negative sign represents the decrement)
Alternate Method We can solve this question by taking values 100 to ease our calculation.-
Take length = breadth = 100
Hence, initial area = 10000
New length = 110 and new breadth = 80
New area =
110×80=8800 ∴ Required percentage
=[]×100=12%.