Question

The sum of digits of two digits numbers is 12.if 18 is added to it.the digits are reversed.find the numbers.

Answer 1

Step-by-step explanation:

Let the unit's digit be $x$

• As the sum of both digits is 12, the ten's digit is $(12 - x)$

∴ The number = $(12 - x) × 10 + x$

• On reversing the digits, we have x at ten's place and $(12-x)$ at unit's place.

∴ New number = $x × 10 + (12 - x)$

According to given information,

⟾ $x \times 10 + (12 - x) = (12 - x) \times 10 + x + 18$

⟾ $10x + 12 - x = 120 - 10x + x + 18$

⟾ $9x + 12 = -9x + 138$

⟾ $9x + 9x = 138 - 12$

⟾ $18x = 126$

⟾ $x = 7$

∴ Unit's digit = 7 and ten's digit = 12-7 = 5

∴ Original Number = 57