Question 1192437
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There are three boys, Cyril, Ryan, and Guye. The sum of their ages is twenty years. 
Cyril’s age added to Guye’s is four-time Ryan’s age, and Ryan’s age added to Cyril’s is four times Guye’s. 
How old are three boys?
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            This problem can be solved  MENTALLY  without using any equations.


            Common sense and mental reasoning is / (are) just enough.



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Indeed, we are given that 

    Cyril’s age added to Guye’s is four-time Ryan’s age.


Add to it the Ryan's age.  You will get five times the Ryan's age.
From the other side, the sum of ages of three boys is 20.
It means that five times the Ryan's age is 20 years - - - hence, Ryan's age is 20/5 = 4 years.


Similar reasoning gives  20/5 = 4 years for the Guye's age.


It leaves  20-4-4 = 12 years for the Cyril's age.
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Solved.