Question

a number is first increased by 15% and then reduced by 15%. By what percent does the number change?​

Answer 1

Answer:

2.25 %

Step-by-step explanation:

Let the number be 'x'

Case 1: Increased by 15 %

⇒ Increased value = ( 15 / 100 ) × x + x

⇒ Increased value = 15x / 100 + x

⇒ Increased value = 0.15x + x = 1.15x

Case 2: Decreased by 15 %

⇒ Decreased value = 1.15x - ( 15 / 100 ) × 1.15 x

⇒ Decreased value = 1.15x - 0.1725x

⇒ Decreased value = 0.9775x

Therefore the value is less than x. Hence the overall result is decreased.

⇒ Decreased Percentage = [( x - 0.9775x ) / x ] × 100

⇒ Decreased Percentage = 0.0225 × 100 = 2.25 %

Hence the number change is decreased by 2.25 %.