MathematicsA number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reserved. Find the number.

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reserved. Find the number.


  1. A
    34
  2. B
    60
  3. C
    63
  4. D
    20 

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    Solution:

    Concept- Assuming two digits as x and y. According to the conditions, we will solve the questions to find the number.
    Number becomes 10x+y
    According to the condition,
    x+y=9…………………………………(i)
    Reversed form of the number,
    =10y+x
    Now, subtracting 27 from the given number and equating its reverse, we will get,
    10x+y-27=10y+x
    10x+y-10y-x=27
    9x-9y=27
    9(x-y)=27
    x-y=3………………………….(ii)
     Adding equation (i) and (ii), we get
    x+y+x-y=9+3
    2x=12
    x=6
    Putting the value of x in equation(i),
    6+y=9
    y=3
    Therefore, number =10x+y
    Number =10×6+3
    Number =63
    Hence, the correct answer is option 3.
     
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