Question:
A number consists of two digits whose sum is 9. If 27 is subtracted from the original number its digits gets interchanged .Find the original number.
Solution:
Let the tens digit of the required number be x and the unit (once) digit of the number be y.
Then;
The original number = 10x + y
Also,
The new number formed after interchanging the digits = 10y + x
Now,
According to the question;
The sum of the digits of the required two-digits number is 9.
ie;
=> x + y = 9
=> y = 9 - x -----------(1)
It is said that ,
If 27 is subtracted from the original number (required number), then its digits gets interchanged.
=> 10x + y - 27 = 10y + x
=> 10x + y - 27 - 10y - x = 0
=> 9x - 9y - 27 = 0
=> 9(x - y - 3) = 0
=> x - y - 3 = 0
=> x - (9 - x) - 3 = 0 {using eq-(1)}
=> x - 9 + x - 3 = 0
=> 2x - 12 = 0
=> 2x = 12
=> x = 12/2
x = 6
Putting the x = 6 in eq-(1) , we get;
=> y = 9 - x
=> y = 9 - 6
=> y = 3
Thus,
Tens digit = x = 6
Unit digit = y = 3
Hence,
Required number = 10x + y
= 10•6 + 3
= 60 + 3
= 63.
The required number is 63.
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Answers & Comments
Question:
A number consists of two digits whose sum is 9. If 27 is subtracted from the original number its digits gets interchanged .Find the original number.
Solution:
Let the tens digit of the required number be x and the unit (once) digit of the number be y.
Then;
The original number = 10x + y
Also,
The new number formed after interchanging the digits = 10y + x
Now,
According to the question;
The sum of the digits of the required two-digits number is 9.
ie;
=> x + y = 9
=> y = 9 - x -----------(1)
Also,
It is said that ,
If 27 is subtracted from the original number (required number), then its digits gets interchanged.
ie;
=> 10x + y - 27 = 10y + x
=> 10x + y - 27 - 10y - x = 0
=> 9x - 9y - 27 = 0
=> 9(x - y - 3) = 0
=> x - y - 3 = 0
=> x - (9 - x) - 3 = 0 {using eq-(1)}
=> x - 9 + x - 3 = 0
=> 2x - 12 = 0
=> 2x = 12
=> x = 12/2
x = 6
Now,
Putting the x = 6 in eq-(1) , we get;
=> y = 9 - x
=> y = 9 - 6
=> y = 3
Thus,
Tens digit = x = 6
Unit digit = y = 3
Hence,
Required number = 10x + y
= 10•6 + 3
= 60 + 3
= 63.
Hence,
The required number is 63.
Here is your answer
and I explained very clearly that u no need to get answer in copy
and give me 20 thanks for my answers
and fol.low me for more best answers in future for u