Question

The sum of the digits of a two-digit number is 8 and the difference between the numbers and that formed by reversing the diguts is 18 find the number

Answer 1

Sol:
Let the number with two digits be 10x + y.
Sum of the digits is 15.
⇒ x + y = 15 ----------------- (1)
Number formed by reversing the digits = (10y + x)

(10x + y) - (10y + x) = 27
⇒ 9x - 9y = 27
⇒ x - y = 3 ----------------- (2)
Solving equations (1) and (2), we get x = 9 and y = 6.

Therefore, the original number is 10(9) + 6 = 96.

Answer 2

Take the number = 10x+y.

 x + y = 8 …(1)

10x+y - (10y+x) = 18 … (ii)

(ii) becomes 10x+y - 10y-x = 18 or

9x -9y = 18, or

x - y = 2 … (iii)

x+y = 8 … (i). Add (i) and (iii) to get

2x = 10, or x = 5. The y = 8–5 = 3

Hence the number is 53. The reverse is 35 and 53–35 = 18.