A number consists of two digits whose sum is 8. If 18 is added to the number it's digits are reversed. Find the number
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A number consists of two digits whose sum is 8. If 18 is added to the number it's digits are reversed. Find the number
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Answer:
let the ones place of the number be X and the tens place of the number be Y
there fore the no. is 10y+x
now,
whenn 18 is added to the nno. the. digits are reversed.
therefore, the new no. is 10x+y.
10x+y + 18 = 10y+x
9x-9y = 18
x-y = 18
x+y = 8
x=13, y = -5
so this no. is not possible.
Step-by-step explanation:
Let the digit at ones place be= x
It is given that the sum of the digits of the number is 8.
Therefore, The digit at tens place = 8-x
Thus, the original number = 10(8-x)+x
=80-10x+x
=80-9x
On interchanging the digits of the given number, the digit at ones place becomes (8-x) and the digit at tens place becomes x.
Therefore, New number= 10x +(8-x)
=9x+8
It is given that when 18 is added to the original number its digits get reversed,
i.e. Original number + 18 = New number
(80-9x) + 18 = (9x+8)
=> 80-9x+18=9x+8
=> 80+18-8 = 9x+9x
=> 90 = 18x
=> x = 90/18
= 5
Hence the original number is,
The digit at ones place= x
= 5
The digit at tens place = 8-x
= 8-5 = 3
Therefore,
Original number = 35 (Ans)