Question

The sum of the digits of a two - digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number. Check your solution.

Answer 1

The sum of two digits = 12

Let the ones digit of the number = x

then tens digit = 12 - x

and number = x + 10 (12 - x)

= x + 120 - 10x = 120 - 9x

Reversing the digits,

ones digit of new number = 12 - x

and tens digit = x

the number = 12 - x + 10 x = 12 + 9x

According to the condition,

$12+9x=120-9x+54\Rightarrow 9x+9x=120+54-12=174-12\Rightarrow 18x=162\Rightarrow x=\frac{162}{18}=9$

$\therefore$ Original number = 120 - 9x

= 120 - 9 $\times$ 9 = 120 - 81 = 39

Hence number = 39 Ans.

Check : Original number = 39

Sum of digits = 3 + 9 = 12

Now reversing its digit the new number will be = 93

and 93 - 39 = 54 which is given.