the sum of the digits of a two-digit number is 11 the number got by interchanging the digits is 27 more than the original number what is this number

Dear student
Let the digit at one's palce is x and the digit at ten's place is yThen originla number=10y+xSum of digits=x+y=11     ...(1)And Acc to question,we have10x+y=27+10y+x9x-9y=27x-y=3    ....(2)Adding (1) and (2), we get2x=14x=7Put the value of x in (1), we get7+y=11y=4So, the original number=10(4)+7=47
Regards

  • -1
Let the digit in unit place be X.
and the digit in ten's pace be (11 - X)

Therefore, the number is
= 10(11 - X) + X
= 110 - 10x + x
= 110 - 9x

And the reversed number is 
=10X + (11 - x)
= 10x + 11 - x
= 9x + 11

now,
according to question,

110 - 9x + 27 = 9x + 11
=> 137 - 9x = 9x + 11
=> 137 - 11 = 9x + 9x
=> 18x = 126
=> x = 126/18
=> x = 7

 therefore, the number is
= 110  - 9x
= 110 - 9 * 7
= 110 - 63
= 47
                                        
  • 2
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