Question

A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 is subtracted
from it, the digits will be reversed. Find the number.
life
sher and
formed​

Answer 1

Let the number between 10 and 100

= 10x + y

It is eight times the sum of its digits ⇒ 10x + y = 8(x + y) ⇒ 2x - 7y = 0 ....(1)

If 45 is subtracted from the number, the digits are reversed.

(10x + y) - 45 = (10y + x)

⇒ 9x - 9y = 45 ⇒ x - y = 5 .....(2)

By solving equations (1) and (2),

7y/2 - y = 5

5y/2 = 5

y = 2

So x = 7

we get x = 7 and y = 2.

Therefore, the original number is 72.