SSC MTS 5 Aug 2019 Shift 2 Paper

Let the side of the square be 100x.
Initial area of square = (100x)${}^2$ = 10000x${}^2$
Side of square after 10 % increase = 100x × (100 + 10)/100 = 110x
Side of square after 20 % decrease = 110x × (100 – 20)/100 = 88x
Initial area of square = (88x)${}^2$ = 7744x${}^2$
Decrease in area = 10000x${}^2$ – 7744x${}^2$ = 2256x${}^2$
Percentage decrease = (2256x${}^2$/10000x${}^2$) × 100 = 22.56 %
Alternate Solution :
Change % = a + b + ab/100
⇒ Change % = 10 – 20 + [10 × (– 20)]/100
⇒ Change % = 10 – 20 – 2 = – 12%
Again,
⇒ Change % = – 12 – 12 + [(– 12) × (– 12)]/100
⇒ Change % = – 24 + 1.44 = – 22.56% (– denotes decrement)
∴ The overall percentage change in area is decreased by 22.56%.