30) The sum of the digit of a two digit number is 12. The number obtai

1.	30) The sum of the digit of a two digit number is 12. The number obtained by interchanging its digit exceedsthe given number by 18. Find the number.
Answer» Given:x + y = 12....(1)10y + x = (10x + y) + 18....(2) 10y - y = 10x - x + 189y = 9x + 18y = x + 2 ...(3)Substituting y = x + 2 in (1) x + (x + 2) = 122x + 2 = 122x = 12 - 22x = 10x = 10/2x = 5substituting in (3) y = 5 + 2y = 7 Thus the number is 57

30) The sum of the digit of a two digit number is 12. The number obtained by interchanging its digit exceedsthe given number by 18. Find the number.

Answer»

Given:x + y = 12....(1)10y + x = (10x + y) + 18....(2)

10y - y = 10x - x + 189y = 9x + 18y = x + 2 ...(3)Substituting y = x + 2 in (1)

x + (x + 2) = 122x + 2 = 122x = 12 - 22x = 10x = 10/2x = 5substituting in (3)

y = 5 + 2y = 7

Thus the number is 57