Question

A number is first increased by 15% and then reduced by 15% .by what percentage does the number change.

Answer 1

Let the number be 100
increased no.= 115
decrease= 115 ×15/100
= 17.25
decreased no. = 115-17.25 = 97.75
change= 100-97.75= 2.25
percent change= 2.25/100×100= 2.25%

Answer 2

Answer:

The number change by 2.25%

Step-by-step explanation:

Let the number be x

Increase % = 15%

New number = $x+\frac{15}{100}x = 1.15x$

Now reduce the obtained number by 15%

Obtained number = $1.15x-\frac{15}{100} \times 1.15x=1.15x-0.1725x=0.9775x$

Difference in new and original number = x - 0.9775x = 0.0225x

Percentage change = $\frac{\text{difference}}{\text{original number}} \times 100$

Percentage change = $\frac{0.0225x}{x} \times 100$

Percentage change = $2.25%$

Hence The number change by 2.25%