Question

Sum of the digits of a two digit number is 12 if the new number by reversing the digit is greater than the original number by 54 find the original number

Answer 1

Question:-

Sum of the digits of a two digit number is 12 if the new number by reversing the digit is greater than the original number by 54 find the original number.

Solution:-

let a and b the digit

a + b= 12          ........(1)

54 + (10a + b) = (10b + a)

54 + 10a + b=10b + a

9a - 9b= -54

a - b= -6        ........(2)

adding (1) and (2)

a + b= 12

a - b= -6

2a=6

a=3

So, b=9

39 + 54= 93 (verified)

Original No.= 39 and No. when digits reversed= 93

Answer 2

Let the original number = x

the sum of two number = 12 - x

original number = 10 ( 12 - x ) + x

after reversing the number = 10x + 12 - x

= A/q

$10x + 12 - x = 10(12 - x) + x + 54 \\ \\ = \geqslant 9x + 12 = 120 - 10x + x + 54 \\ \\ = \geqslant 9x + 9x = 120 + 54 - 12 \\ \\ = \geqslant 18x = 162 \\ \\ = \geqslant x = \frac{162}{18} \\ \\ = \geqslant 9$