Question

A number between 10 and 100 is 8 times the sum of its digits. If 45 is substracted

from it, the result equals the number formed by interchanging its digit. Find the
number

Answer 1

72

Explanation:

Let the number be
`xy`

Value of number =
`10x+y`

`10x+y=8(x+y)`

`10x+y=8x+8y`

`2x-7y+0........(1)`

`10x+y-45=10y+x`

`9x-9y=45`

`x-y=5............(2)`

Multiply by
`-2`

`-2x+2y=-10`

Add to
`(1)`

`-5y=-10`

`y=2`

`x-y=5`

`x-(2)=5`

`x=7`

Number = 72

hope this helps...