Question

A certain number between 10 and 100 is 8 times the sum of its digits and if 45 is subtact from it.the digits is reversed .find the number.

Answer 1

The answer is 72

As it is 8 times the sum of its digits:

7+2 = 9 and

9*8=72

Again digit reversed if subtracted by 45:

72-45= 27

Answer 2

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

the is obviously consists of two digits as the numbers between 10 to 100 are start from 11 and end to 99...

now ...let the one's place digit is =X

and the 2nd place digit is =y

now, the number is =10y+X

....now according to the problem

10y+X=8(X+y)

=>10y+X=8x+8y

=>2y=7x

=>y=7x/2

now ...10y+x-45=10x+y

=>9y=9x+45

=>y=X+5

=>(7x/2)-x=5

=>5x=10

=>X=2

therefore...y=5+2=7

therefore the number is =72