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The area of square is equal to area of rectangle. If length of rectangle is increased by 40% and breadth is decreased by 25%, then what is percentage change in area of square?
  • a)
    20%
  • b)
    10%
  • c)
    5%
  • d)
    8%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The area of square is equal to area of rectangle. If length of rectang...
GIVEN:
Area of Square = Area of Rectangle
Length of rectangle is increased by 40%
Breadth of rectangle is decreased by 25%
FORMULA USED:
Area of rectangle = L × B
Area of square = (side)2
CALCULATION:
Let L be length of rectangle and B be breadth of rectangle.
Given,
LB = (side)2
Given,
New length = L + L × 40/100
= 7L/5
New breadth = B - B × 25/100
= 3B/4
New area of rectangle =
= (7L/5) × (3B/4)
= LB × (21/20)
New Area of square = (side)2 × 21/20
Required percentage change in area =
= {[(21/20) – 1]/1} × 100
= 5%
ALTERNATIVE METHOD:
Required percentage change in area = x + y + x × y / 100
⇒ 40 + (-25) + 40 × -25 / 100 = 5% 
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Most Upvoted Answer
The area of square is equal to area of rectangle. If length of rectang...
GIVEN:
Area of Square = Area of Rectangle
Length of rectangle is increased by 40%
Breadth of rectangle is decreased by 25%
FORMULA USED:
Area of rectangle = L × B
Area of square = (side)2
CALCULATION:
Let L be length of rectangle and B be breadth of rectangle.
Given,
LB = (side)2
Given,
New length = L + L × 40/100
= 7L/5
New breadth = B - B × 25/100
= 3B/4
New area of rectangle =
= (7L/5) × (3B/4)
= LB × (21/20)
New Area of square = (side)2 × 21/20
Required percentage change in area =
= {[(21/20) – 1]/1} × 100
= 5%
ALTERNATIVE METHOD:
Required percentage change in area = x + y + x × y / 100
⇒ 40 + (-25) + 40 × -25 / 100 = 5% 
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