Question

If the length of a rectangle is decreased by 50% and the breadth is increased by 80%, then
the % change in the area of rectangle is
(A) decreased by 10%
(B) increased by 10%
(C) decreased by 20%
(D) increased by 20%

Answer 1

option b is correct

Answer 2

Answer:

option  (A) is correct

Step-by-step explanation:

Let l and b be the length and breadth of the rectangle.

As per data,

New length

= l - 50% of l

= l - (50/100)l

= l - l /2

= l /2

New breadth

= b + 80% of b

= b + (80/100)b

= b + (4/5)b

=9b/5

New area of the rectangle

= (New length)(New breadth)

=(l/2)(9b/5)

=(9/10)lb

since (9/10)lb < lb, area of the rectangle is decreased.

Change in area

= lb - (9/10)lb

= (1/10)lb

Percentage of change in area

$=\frac{new\:area}{original\:area}(100)\\\\=\frac{\frac{1}{10}lb}{lb}(100)\\\\=\frac{1}{10}(100)$

= 10%

Therefore the area is decreased by 10%