Question

A certain number between 10 and 100 is 8 times the sum of its digit and if 45 is subtracted from 8 digit will be reversed find the number. how we come to know that equation first and equation second will subtracted or added in this equation. explain briefly. ​

Answer 1

First Equation :

Given: the number is 8 times the sum of digit

Let the digit in ones place be y and tens place be x

let the number be = [10x+y]

8 times sum of its digit will be= [8(x+y)]

so

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

which solves to

$0 = 2x - 7y$

Second Equation :

Given : if 45 is subtracted from it it will be reversed.

The number is = [10x+y]

If it is subtracted (-) from 45

It will become reversed = [10y+x]

so,.

$10x + y - 45 = 10y + x$

which solves to

$5 = x - y$

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Refer the attachment for solution