Question

Sum of the digits of a two digit number is 12. New number formed by reversing the digit is greater than the original number by 54. Find the original number.

Answer 1

Let one’s digit be x.

Since the sum of digits is 12.

Therefore, ten’s digit = (12 – x) ….(i)

∴Number = 10 x ten’s digit + One’s digit

= 10 (12 – x) + x

= 120 – 10x + x

= 120 – 9x

Now, if digits are reversed, then

One’s digit = 12 – x and ten’s digit = x

∴ New number = 10 x ten’s digit + one’s digit

= 10(x) + 12 – x

= 10x + 12 – x

= 10x – x + 12

= 9x + 12

According to question,

⇒ 9x + 12 = (120 – 9x) + 54

⇒ 9x + 12 = 120 + 54 – 9x

⇒ 9x + 12 = 174 – 9x

⇒ 9x + 9x = 174 – 12

⇒ 18x = 162

⇒ x = 162/18

⇒ x = 9

One’s digit = 9 and ten’s digit = 12 – 9 = 3

Hence, the required number = 39.