Question

The sum of the digits of a two digit number is 9. If the digits are exchanged the new number obtain is 9 less than the three times of the original number. find the two digit number.

Answer 1

Let the digit at tens place is 'y' and the digit at units place is 'x'.

So, the original number = 10y + x.

The number formed on interchanging the digits = 10x + y.

Given that sum of digits of a two digit number is 9.

= > x + y = 9.     ------ (1)

Given that the number obtained is 9 less than the three times the original.

= > 10x + y = 3(10y + x) - 9

= > 10x + y = 30y + 3x - 9

= > 10x + y - 30y - 3x = -9

= > 7x - 29y = -9      ---------- (2)

On solving (1) * 7 & (2), we get

= > 7x + 7y = 63

= > 7x - 29y = -9

   -----------------------

    36y = 72

        y = 2.

Substitute y = 2 in (1), we get

= > x + y = 9

= > x + 2 = 9

= > x = 7.

Therefore, the 2 digit number is 10y + x = 10(2) + 7 = 27.

Hope it helps!