Question

the sums of a two digit number is 6. when the digits are reversed the new number is 36 more than the original number. find the original number

Answer 1

Let
x and y are two digits of a number
number = n

Sum of the digits
x+y=6.....................(1)
When x is ten and y is unit
10x+y=n.............(2)
When the digits are reversed, the new number is 36 more than the original number
Now y is ten and x is unit
10y+x=n+36.............(3)
Subtract (2) from (3)
10y+x=n+36.............(3)
-10x-y=-n.............(2)

-9x+9y=36
9(y-x)=36
9(y-x)/9=36/9
y-x=4...................(4)
Add (1) and (4)
y-x=4...................(4)
x+y=6.....................(1)

2y=10
2y/2=10/2
y=5
Put the value of y in (1)
x+5=6.....................(1)
x=6-5
x=1
Number = 15
When the digits are reversed = 51 (15+36=51)