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
Solution :
Let the unit digit = x
Ten’s digit = 12 –x
Original number = 10( 12 –x ) + x
= 120 – 10x + x
Original number = 120 – 9x
Reversing the digits :
Unit digit = 12 – x
Ten’s digit = x
New number = 10x + 12 – x
New number = 9x +12
As new number is less than the original number by 54
9x +12 = 120 – 9x -54
9x +12 = 66 – 9x
9x + 9x = 66 -12
18 x = 54
X = 3
Original number = 120 – 9x
= 120 – 9(3)
= 120 – 27
Original number = 93