A number is increased by 20% and the increased number is decreased by 20%. Find the increase or decrease percent.

By Ritesh|Updated : November 8th, 2022

A number is increased by 20% and the increased number is decreased by 20%. The net percent decrease is 4%. Let x be the number:

Increase in the number = 20% of x

= 20/100 x x

= 15 x x

= x/5

Increased number = x + x/5

= (5x + x)/5

= 6x/5

The resulting figure fell by 20%.

Decrease in the number = 20% of 6x/5

= ⅕ x 6x/5

= 6x/25

New number = 6x/5 - 6x/25

= (30x - 6x)/25

= 24x/25

Net decrease = x - 24x/25

= (25x - 24x)/25

= x/25

Net % decrease = x/25/x x 100

= x/25 x 1/x x 100

= 4%

Formula for Percentage

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Percent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

As follows is the percentage formula:

Percentage = (Value ⁄ Total Value) × 100

Hence, the net percentage decreased by 4%

Summary:

A number is increased by 20% and the increased number is decreased by 20%. Find the increase or decrease percent.

20% of a number is added, and 20% of the added number is subtracted. The overall decline is 4%. The formula to calculate the percentage of a quantity in terms of 100 is the ratio of value to total value multiplied by 100.

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