Question

a number is increased by 10% and decreased by 10% what is the net gain or loss percent​

Answer 1

Answer: 1%

Step-by-step explanation:

Assume the number to be 100 for instance,

10% of 100 increased = 100 + ( 10 / 100*100 )

=> 100 + 10 = 110

The resulting number decreased by its 10% = 110- (10/100*110)

=> 110-11 = 99

Now, net decrease => 100-99 = 1

Decrease percent = (Decrease / Original number * 100) %

=> ( 1 / 100 *100 )%

=> 1%.

Answer 2

Let the number be x .

If we increase the number by 10% then the new number formed will be the following :-

⇒ x + 10% of x

⇒ x + 10/100 × x

⇒ x + x/10

⇒ ( 10 x + x )/10

⇒ 11x/10

This number will be decreased by 10 % .

The resultant number will be :-

⇒ 11x/10 - 10% of 11x/10

⇒ 11x/10 - 10/100 × 11x/10

⇒ 11x/10 - 11x/100

⇒ ( 110 x - 11 x ) / 100

⇒ 99 x / 100

Net change = x - 99x/100

⇒ ( 100 x - 99 x ) / 100

⇒ x/100

The number decreased from x to 99x/100

Decrease % = decrease / original × 100

⇒ ( x/100 ) / ( x ) × 100

⇒ 100/100 %

⇒ 1%

The decrease percentage is 1 % .