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Q.

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
 


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a

36

b

65

c

63

d

56 

answer is A.

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Detailed Solution

It is given that sum of the digits of a two-digit number is 9.
Let the unit place digit of two numbers is x.
Hence, tens place digit =9-x.
Original number =x+10(9-x).
New digit number (Interchanging the digits) = 10x+(9-x).
New number = original number +27.
Substitute the value of the new digit number and the original number in equation ,
⇒10x+(9−x)=10(9−x)+x+27  
Solve the bracket,
⇒10x+9−x=90−10x+x+27 ⇒9x+9=117−9x  
Transpose (-9x) to the left-hand side and 9 to the right-hand side.
  ⇒9x+9x=117−9 ⇒18x=108 ⇒x= 108 18 ⇒x=6  
The unit digit is 6.
The required number will be,
=6+3×10 =6+30 =36  
The two-digit number is 36.
Correct option is 1.
 
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