Question 1116799
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The algebraic solution provided by the other tutor is of course fine; and perhaps you needed to see an algebraic solution.<br>
But you can get some good mental exercise from solving this problem using logical reasoning.<br>
Think about it.  If the difference in their ages is 2 years, and 5 years ago Luke was 3/5 of his friend's age, then their ages 5 years ago had to be 3 and 5.<br>
So their present ages are 8 and 10.