Question

a number first increased by 15% and then decreased by 15% By what percentage does the number change pls solve it step by step and send me ​

Answer 1

Given :-

A number first increased by 15% and then decreased by 15% .

To find :-

By what percentage does the number change .

Solution :-

Let the number be X

The increased percentage in the number = 15%

Increasing in the number = 15% of X

= (15/100)×X

= (3/20)×X

= 3X/20

The number will be X+(3X/20)

= (20X+3X)/20

= 23X/20

The decreased percentage in the number = 15%

Decreasing in the number = 15% of (23X/20)

= (15/100)×(23X/20)

= (3/20)×(23X/20)

= (3×23X)/(20×20)

= 69X/400

The new number = (23X/20)-(69X/400)

LCM of 20 and 400 = 400

= [(23X×20)-(69X×1)]/400

= (460X-69X)/400

= 391X/400

The original number = X

The new number = 391X/400

X > 391X/400

So it is decreased

The decreasing in the number

= X-(391X/400)

= (400X-391X)/400

= 9X/400

The decreased percentage in the number

=(Decreasing in the number/Original number)×100

= [(9X/400)/X]×100

= (9X/400X)×100

= (9/400)×100

= (9×100)/400

= 900/400

= 9/4 or

= 2 1/4 or

= 2.25

Answer :-

The number is decreased by 9/4% or 2 1/4% or 2.25%