SOLUTION: The sum of the digits of a two-digit number is 6. When the digits are reversed, the new number is 36 more than the original number. Find the number.

Question 570234: The sum of the digits of a two-digit number is 6. When the digits are reversed, the new number is 36 more than the original number. Find the number.

Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
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)
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