The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18.Find the NEW number
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Answer:
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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.
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Step-by-step explanation:
Given:-
The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18.
To find:-
Find the new number?
Solution:-
Let the digit at 10's place be X
The value of X = 10X
Let the digit at 1's place be Y
The value of Y =Y
Then the number = 10X+Y
If the digits are reversed then the new number
=10Y+X
Given that
The sum of the digits of the two digits number
=8
X+Y = 8-------------(1)
and
The difference between the number and that formed by reversing the digits =18
=> (10X+Y) -(10Y+X) = 18
=> 10X+Y-10Y-X = 18
=> (10X-X)+(Y-10Y) = 18
=> 9X-9Y=18
=>9(X-Y) = 18
=>X-Y=18/9=2
X-Y = 2------------(2)
On adding (1)&(2)
X+Y = 8
X-Y = 2
(+)
________
2X+0=10
________
2X = 10
=>X = 10/2
X=5
On substituting the value of X in (1) then
X+Y = 8
=>5+Y = 8
=>Y = 8-5=3
Y = 3
X= 5 and Y = 3
The number = 53
The new number = 35
Answer:-
The original number = 53
The new number obtained by reversing the digits = 35
Check:-
The number = 53
Sum of the digits = 5+3=8
New number = 35
Their difference = 53-35 = 18
Verified the given relations.