A rectangle was altered by increasing its length by 20 percent and decreasing its width by X percent. If these alterations decreased the area of the rectangle by 4 percent, what is the value of X?

A) 12

B) 15

C) 20

D) 22

Solution:

Choice C is correct.

Let l and w be the length and width of the original rectangle respectively. Hence, the area of original rectangle is lw.

Since, the length is increased by 20% and width is decreased by X% Altered length = 1.2l

And altered width = (1 – X/100)w

Since, these alterations decrease the original area by 4% = (1 – .04) lw = .96lw

Therefore, .96 lw = (1.2l) (1- X/100)w

Or X = 20.