Question

See the third question

Answer 1

Let the digit at tens place be x and the digit at units place be y.

Then the original two digit number = 10x + y.

Given that it is 8 times the sum of its digits.

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

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

= > 2x = 7y

= > x = (7/2)y   ------ (1)

Given that if 45 is subtracted from it, the digits will be reversed.

= > 10x + y - 45 = 10y + x

= > 10x - x - 10y + y = 45

= > 9x - 9y = 45

= > x - y = 5

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

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

= > 5y/2 = 5

= > 5y = 10

= > y = 2.

Substitute y = 2 in (1), we get

= > x = (7/2)y

= > x = (7/2) * 2

= > x = 7.

Therefore, the number is 72.

Hope this helps!