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the sum of the digits of a two-digit number is 7. the number obtained by interchanging the digits exceeds the original number by 27.find the number.

please.i want the full explaination of this question...!!

let the no . be 10x + y 

therefore 10x + y = 7 

atq 10y +x = 27

now u cn well solve

hopw this helped :)

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Let the unit digits of the  number be x
Then, tens digit of the number = 7 - x
Original number = 10(7-x) + x = 70 - 10x + x = 70 - 9x
When digits are  interchanged-
The units digit = (7-x) 
The tens digint= x
The number = 10*x + (7-x) = 10x + 7 - x = 9x + 7
As per question - 
(9x + 7) - 27 =  70 - 9x
=> 9x - 20 = 70 - 9x
=> 9x + 9x = 70 + 20
=> 18x = 90
=>x = 90/18 = 5
 
Then, the units digit of original number = x = 5
Tens digit of original number =  7-x = 7 - 5 = 2
Therefore, original number is 25.
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25
 
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