Question

A number is increased by 10% and then the increased number is dicreased by 10%find the net increased or decreased percentage

Answer 1

Greetings..!!

Let the required number be x .

First increase = 10% = 10% of x = (10/100)*x = 10x/100 = x/10

So, new number = Previous + Increase = x + x/10 =  11x/10

Now, decrease = 10% = 10% of 11x/10 = (10/100)*(11x/10) = 11x/100

New number = previous number - decrease = (11x/10)-(11x/100) = (110x-11x)/100 = 99x/100

Let's compare the original number and the resulting number by making their denominators equal :

L.C.M of 1 ( from original number x) and 100(from resulting number 99x/100)  = 100

Let's make the denominators equal ,

x*100/1*100 = 100x/100 ||||| And already the denominators of 99x/100 is 100.

Clearly, 100x/100 > 99x/100 by x/100

So, net increase = x/100

original number =x

So, net increase % = (increase ÷ original no)*100 =  (x/100 ÷ x)*100=( x/100*1/x)*100 =  1%

Answer : Hence , net increase percentage is 1%.