the sum of two digit number is 9. when we interchange the digits we found that the resulting digit is greater than the original digit by 27. find the two digit number.
Answers
Given :-
• The sum of the digits of a two digits number is 9.
• After interchanging the digits, it is found that the resulting new number is greater than the original number by 27.
To Find :-
• What is the two - digit number?
Solution :-
Let the number at ones place of two digit number be x.
As per question :-
Given that,
The sum of the digits of a two digits number is 9.
Therefore,
the number at tens place will be (9-x).
And the number will be = 10 ( 9-x) +x
After interchanging the digits :-
The number will be = 10x + (9-x)
According to the question :-
New number -27 = Original number
⟼ 10x +(9-x) -27 = 10( 9-x) +x
⟼ 10x +9 -x -27 = 90 -10x +x
⟼ 9x -18 = 90 -9x
⟼ 18x = 108
Therefore,
digit at ones place is = 6
and digit at tens place is
= 9-x
= 9-6
= 3
The two digit number is
= 10 ( 9-x) +x
= 10 ( 9-6) +6
= 36
Hence, the two digit number is = 36.
Answer:
Given :-
• The sum of the digits of a two digits number is 9.
• After interchanging the digits, it is found that the resulting new number is greater than the original number by 27.
To Find :-
• What is the two - digit number?
Solution :-
Let the number at ones place of two digit number be x.
As per question :-
Given that,
The sum of the digits of a two digits number is 9.
Therefore,
the number at tens place will be (9-x).
And the number will be = 10 ( 9-x) +x
After interchanging the digits :-
The number will be = 10x + (9-x)
According to the question :-
New number -27 = Original number
⟼ 10x +(9-x) -27 = 10( 9-x) +x
⟼ 10x +9 -x -27 = 90 -10x +x
⟼ 9x -18 = 90 -9x
⟼ 18x = 108
⟼x = 6⟼x=6
Therefore,
digit at ones place is = 6
and digit at tens place is
= 9-x
= 9-6
= 3
The two digit number is
= 10 ( 9-x) +x
= 10 ( 9-6) +6
= 36
Hence, the two digit number is = 36.