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 Nanyang SA1 2011 Q30
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By: keenlearner (offline)  Friday, November 09 2012 @ 06:35 AM CST (Read 826 times)  
keenlearner

Hi everyone, appreciate help with this problem sum:

Ali, Bala and Carl shared 90 marbles. If Ali gave 6 marbles to Bala, Bala gave 2 marbles to Carl and after that Carl gave 1/4 of what he had to Ali, the three boys will have the same number of marbles in the end. How many more marbles than Ali did Carl have?

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By: jo sarah (offline)  Saturday, November 10 2012 @ 08:03 AM CST  
jo sarah

Ali, Bala and Carl shared 90 marbles. If Ali gave 6 marbles to Bala, Bala gave 2 marbles to Carl and after that Carl gave 1/4 of what he had to Ali, the three boys will have the same number of marbles in the end. How many more marbles than Ali did Carl have?

[this is a 'work-backward' type of question.]

in the end, all 3 has same no. Therefore, each will have 90 / 3 = 30 marbles in the end.

........................Ali..................Bala..................Carl
in end:.............30....................30.....................30................this is after C gives 1/4 to A, i.e, what C has is 3/4 --> 30; 1/4 --> 10
A return to C:..-10............................................+10
giving;.............20....................30.....................40.................this is after B gives 2 to C
C return to B:...........................+2.....................-2
giving:.............20....................32.....................38.................this is after A gives 6 to B
B return to A:...+6....................-6..........................
resulting in:......26....................26....................38.................which is what each boys have actually. [Notice the 2nd sentence starts with a "If"]

therefore, Carl has 38 - 26 = 12 more marbles than Ali. Big Grin

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