Sum of the digits of two digit number is 11. when we interchange the digits it is found that the resulting number is less than the original number by 9. what is the two digit number?
Sum of the digits of two digit number is 11. when we interchange the digits it is found that the resulting number is less than the original number by 9.
To Find :-
Original number
Solution:-
Let,
Unit place = x
Tens place = (11 - x)
[tex]\sf Original\:Number =10(11-x)+x[/tex]
[tex]\sf Original\:Number=110-10x+x[/tex]
[tex]\sf Original\:Number=110-9x[/tex]
[tex]\sf Interchanged\:Number =10(x)+11-x[/tex]
[tex]\sf Interchanged\:Number=10x+11-x[/tex]
[tex]\sf Interchanged\:Number=9x+11[/tex]
Now,
On subtracting original number and interchanged number we get 8
Answers & Comments
Verified answer
Step-by-step explanation:
Given :-
Sum of the digits of two digit number is 11.
If interchange the digits of then the resulting number is less than the original number by 9.
To find :-
The two digit number.
Solution :-
Let the digit at tens place be X
The place value of X = 10×X = 10X
Let the digit at ones place be Y
The place value of Y = 1×Y = Y
The two digit number = 10X+Y
Given that
Sum of the digits of two digit number = 11
Therefore, X+Y = 11 --------------(1)
If the digits are interchanged then othe new number = 10Y+X
According to the given problem
If interchange the digits of then the resulting number is less than the original number by 9.
=> Original number = New number -9
=> 10X+Y = 10Y+X-9
=> 10X+Y-10Y-X = -9
=> (10X-X)+(Y-10Y) = -9
=> 9X-9Y = -9
=> 9(X-Y) = -9
=> X-Y = -9/9
=> X-Y = -1
Therefore, X-Y = -1 ---------------(2)
On adding (1) & (2) then
X+Y = 11
X-Y = -1
(+)
________
2X+0 = 10
________
=> 2X = 10
=> X = 10/2
=> X = 5
Therefore, The digit at tens place = 5
On substituting the value of X in (1) then
=> 5+Y = 11
=> Y = 11-5
=> Y = 6
Therefore, The digit at ones place = 6
Therefore, The two digit number = 56
Answer:-
The required two digit number is 56
Check:-
The two digit number = 56
The digit at tens place = 5
The digit at ones place = 6
The sum of the digits = 5+6 = 11
The number obtained by reversing the digits = 65
=> 65-9
=> 56
=> Original number = New number -9
Verified the given relations in the given problem.
Answer:
65
Step-by-step explanation:
Given :-
Sum of the digits of two digit number is 11. when we interchange the digits it is found that the resulting number is less than the original number by 9.
To Find :-
Original number
Solution :-
Let,
Unit place = x
Tens place = (11 - x)
[tex]\sf Original\:Number =10(11-x)+x[/tex]
[tex]\sf Original\:Number=110-10x+x[/tex]
[tex]\sf Original\:Number=110-9x[/tex]
[tex]\sf Interchanged\:Number =10(x)+11-x[/tex]
[tex]\sf Interchanged\:Number=10x+11-x[/tex]
[tex]\sf Interchanged\:Number=9x+11[/tex]
Now,
On subtracting original number and interchanged number we get 8
[tex]\sf\implies 110-9x-(9x+11)=9[/tex]
[tex]\sf\implies 110-9x-9x-11=9[/tex]
[tex]\sf\implies 99-18x=9[/tex]
[tex]\sf\implies 99-9=18x[/tex]
[tex]\sf\implies 90=18x[/tex]
[tex]\sf\implies \dfrac{90}{18}=x[/tex]
[tex]\sf\implies 5=x[/tex]
[tex]\sf\implies Number =110-9(5)[/tex]
[tex]\sf\implies Number=110-45[/tex]
[tex]\sf\implies Number = 65[/tex]
Hence,
The original number is 65