Question

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 8. Find the number.

Answer 1

Let units digit = x
Tens digit = y
So, the original number is = unit digit + 10 × tens digit
= x + 10y
According to question,
Sum of digits = 8
so, x + y = 8 . . . (i)
On reversing the digits, new number = 10x + y
According to question
Difference = 18
⇒ x+10y−(10x+y)=18
⇒ x+10y−10x−y=18
⇒ 9y−9x=18
⇒ y−x=2 . . . (ii)
By adding eq. (i) and (iii)
2y = 10
y=10/2⇒y=5
Put the value of y in eq. (i)
⇒ x+y=8
⇒ x+5=8
⇒ x=8−5
⇒ x=3
∴ Original number =10y+x
=10×5+3
=50+3
=53