Sum of the digits of a two-digit number is 8.
When we interchange the digits, it is found that the resulting new number is less than the original number by 54.
What is the two-digit number?
Answers
Answer:
Let x be the digit at unit’s place and y be the digit at ten’s place.
Since y is at ten’s place, then the number formed is 10y+x.
By reversing the digits, it becomes 10x+y.
As the difference of the numbers is 18, so,
(10y+x)−(10x+y)=18
9(y−x)=18
y−x=2 .... (1)
As the sum of digits is 8, so,
x+y=8 .... (2)
On adding equations (1) and (2), we get
2y=10⇒y=5
Putting this in (2), we get x=8−5=3
x=3,y=5
Hence, number =10y+x=10×5+3=53.
Step-by-step explanation:
Let x be the digit at unit’s place and y be the digit at ten’s place.
Since y is at ten’s place, then the number formed is 10y+x.
By reversing the digits, it becomes 10x+y.
As the difference of the numbers is 18, so,
(10y+x)−(10x+y)=18
9(y−x)=18
y−x=2 .... (1)
As the sum of digits is 8, so,
x+y=8 .... (2)
On adding equations (1) and (2), we get
2y=10⇒y=5
Putting this in (2), we get x=8−5=3
x=3,y=5
Hence, number =10y+x=10×5+3=53.