Sum of the digits of a two digits number is 12. New number formed by reversing the digit is greater than the original number by 54. Find the original number .
Answers
Tens = 12-x
No.formed = 10(12-x)+x = 120-9x
After digits get interchanged
Ones = 12-x
Tens = x
No.formed = 10x+12-x = 9x+12
ATQ
New no. - old no. = 54
9x+12 - (120-9x) = 54
9x+12-120+9x = 54
18x-108 = 54
18x = 162
x = 9
Original no. = 120-9x = 120-81 = 39
Ans= 39
Answer :-
The original number is 39.
Solution :-
Let the digits of the number be x and y
Sum of the digits of a two digit number = 12
⇒ x + y = 12
⇒ x = 12 - y ---(1)
Two digit number = 10(x) + y = 10(12 - y) + y= 120 - 10y + y = 120 - 9y
Number when digits are reversed = 10y + x = 10y + (12 - y) = 10y + 12 - y = 9y + 12
Given
Number when digits are reversed is greater than the original number by 54
It means
Difference between number when digits are reversed original number = 54
⇒ 9y + 12 - (120 - 9y) = 54
⇒ 9y + 12 - 120 + 9y = 54
⇒ 9y - 108 = 54
⇒ 18y = 54 + 108
⇒ 18y = 162
⇒ y = 162/18
⇒ y = 9
Substitute y = 9 in eq(1)
⇒ x = 12 - y
⇒ x = 12 - 9
⇒ x = 3
Substitute x = 3 and y = 9 in 10x + y to find the original number
Original number = 10x + y
= 10(3) + 9
= 30 + 9
= 39
Therefore the original number is 39.
Answer :-
The original number is 39.
Solution :-
Let the digits of the number be x and y
Sum of the digits of a two digit number = 12
⇒ x + y = 12
⇒ x = 12 - y ---(1)
Two digit number = 10(x) + y = 10(12 - y) + y= 120 - 10y + y = 120 - 9y
Number when digits are reversed = 10y + x = 10y + (12 - y) = 10y + 12 - y = 9y + 12
Given
Number when digits are reversed is greater than the original number by 54
It means
Difference between number when digits are reversed original number = 54
⇒ 9y + 12 - (120 - 9y) = 54
⇒ 9y + 12 - 120 + 9y = 54
⇒ 9y - 108 = 54
⇒ 18y = 54 + 108
⇒ 18y = 162
⇒ y = 162/18
⇒ y = 9
Substitute y = 9 in eq(1)
⇒ x = 12 - y
⇒ x = 12 - 9
⇒ x = 3
Substitute x = 3 and y = 9 in 10x + y to find the original number
Original number = 10x + y
= 10(3) + 9
= 30 + 9
= 39