2. The tens digit of a two-digit number is one more the ones digit. If the digits are interchanged,the new number becomes 9 less than the original number. Find the number.
Answers
Answer :
98 , 87 , 76 , 65 , 54 , 43 , 32 , 21 , 10
Solution :
Let the tens digit and the ones digit of the original number be x and y respectively .
Thus ,
Original number = 10x + y
Now ,
After interchanging the digits of original numer ,
New number = 10y + x
Also ,
It is given that , if the digits of the original numer are interchanged , then the new number so obtained is 9 less than original numer .
Thus ,
=> New number = Original numer - 9
=> 10y + x = 10x + y - 9
=> 10x + y - 9 - x - 10y = 0
=> 9x - 9y - 9 = 0
=> 9(x - y - 1) = 0
=> x - y - 1 = 0
=> x = y + 1 ---------(1)
Also ,
It is given that , the tens digit is one more than the ones digit .
Thus ,
x = y + 1 --------(2)
Clearly ,
eq-(1) and (2) are identical , thus there exists many numbers which satisfy the given two conditions .
Such numbers are : 98 , 87 , 76 , 65 , 54 , 43 , 32 , 21 , 10
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