question_answer

A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Which of the given steps is CORRECT to find the number?       

Step 1: Let the unit's digit be x

Step 2: Then, ten's digit \[=(9-x)\] \[\therefore \] Number \[=10\times (9-x)+x\] \[\Rightarrow \] \[90-10x+x=(90-9x)\]

Step 3: Adding 27 to the number \[90-9x,\] we get \[117-9x~\]

Step 4: Number with digits interchanged is \[10x+(9-x)=9x+9\]

Step 5:  \[117-9x=9x+9\]

Step 6: Therefore unit's digit = 6 and ten's digit = 3

Step 7: Hence the number = 36.

A)  Only Step 4

B)         Both Step 1 and Step 2

C)         Step 1, 2, 3 and 4

D)         All steps are correct