Question

A two digit number is four times the sum of its digits. If 27 is added to the number the digits are reversed, find the number.

Answer 1

let the digits be x,y
so according to question
10x+y= 4(x+y) 
⇒10x+y=4x+4y
⇒6x-3y=0
⇒2x-y=0 ......... (i)
again,
10x+y+27=10y+x 
⇒9x-9y +27= 0
⇒x-y+3=0  .......................(ii)
substracting (ii) from (i)
⇒2x-y-x+y-3=0 
⇒x = 3
in (ii)
⇒3-y+3=0
⇒y=6
so the number is 36

Answer 2

let the 2 digit number be in the form of 10x+y where x and y intergers.
now , acc. to question
a 2 digit number that is (10x+y) is 4 times the sum of the digits that is 4(x+y) ..
now, if 27 is added to the number thats is 27+10x+y  then the digits are reversed that is 10y+x...

therefore,
10x+y=4(x+y)
10x+y=4x+4y
10x-4x=4y-y
6x=3y
2x=y
2x-y=0 ---------------------- (1)

now ,
27+10x+y=10y+x
27+10x-x+y-10y=0
9x-9y= -27
9(x-y)= -27
x-y= -3 ------------------ (2)
now , we have 2 simuntaneous equations,
2x-y=0
x-y=3

2x-y=0
2(x-y)=2(-3)

2x-y=0
2x-2y= -6
-   +    +
_______
       y=6

now , putting the value of y=6 in equation (2) ,
x-y= -3
x-6= -3
x= -3 + 6
x=3

therefore the number = 10x+y = 10(3) + (6)
                                            =30+6
                                             = 36