The Sum Of The Digits Of A Two-digit Number Is Five. When The Digits Are Reversed, The Number Exceeds Three Times The Original Tens Digit By Two. What Are The Two Numbers?

Let the nos.be x and y

x - unit's digit

y-ten's digit

x+y=5 (equation no.1)

10x+y=3y+2 (equation no. 2)

simplified: 10x-2y=2 (equation no. 2)

multiply 1st equation by 2 :   2x+2y=10  (equation no. 3)

add equations 3 and 2 : 12x=12 [ as the y gets cancelled : -2y+ (+2y) ]

divide both sides by 12 : X=1

from our 1st equation : Y=5-1

  y=4

the 2 digit no. Is 41.

you can check your answer :

Reversed no. Is 14, and it does exceed 3 time the original tens digit ( 3 * 4 =12) by 2