Question 354523
Three times the tens digit of a certain two-digit number is two more than four times the units digit. The difference between the number given and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number?

let the number be xy
10x+y
..
3x=4y+2
3x-4y=2.........................1
10x+y-10y-x=2(x+y)-2
9x-9y=2x+2y-2
7x-11y=-2.......................2
multiply equation 1 by -7 and equation 2 by 3
-21x+28y=-14
21x-33y=-6
Add the two equations
-5y=-20
y =4
plug the value of y in equation 1
3x=16+2
3x=18
x= 6
number is 68.
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