When a number is increased by 5% and the result decreased by 9%, the answer is 11466. Find the number.

Question

This was a question from a book, the answer is 12000, but I want to see the working out for it.

 

 

Thank you.

Answer 1

x=the number

(x+5%x)-9%(x+5%x)=11,466

x+0.05x-0.09(x+0.05x)=11,466

x+0.05x-0.09x-0.0045x=11,466

1.05x-0.09x-0.0045x=11,466

0.96x-0.0045x=11,466

0.9555x=11,466

x=11,466/0.9555

x=12,000

Answer 2

Let x = the original number

 

The number increased by 5% = x + 0.05x = 1.05x

 

Decrease 1.05x by 9%:   1.05x - 0.09(1.05x) = 0.9555x = 11,466

 

                                                                                x = 11,466 / 0.9555 = 12,000