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 Red Swastika 2011 SA2
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By: manhan (offline)  Tuesday, July 24 2012 @ 04:01 AM CDT (Read 768 times)  
manhan

Question:

Eugene, Freddy and George had some playing cards. Freddy had 200 more playing cards than Eugene, George had 3/4 the number of cards Freddy had. After George lost 1/6 of his cards to Eugene, he had 320 fewer cards than Eugene. What was the ratio of the number of cards Eugene had to the number of cards Freddy had to the number of cards George had in the end?

Answer given: 97:104:65

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By: echeewh (offline)  Tuesday, July 24 2012 @ 10:03 PM CDT  
echeewh

hey manhan,

Following pls find my worked solution:

*** - Buffer space for alignment purpose

<Before>

E |---------------------|<200>*****--> 4p - 200
F |-------|-------|-------|-------|*****--> 4p
G |-------|-------|-------|***********--> 3p

<Process>
G lost (1/6) to E, thereby G would have left with (5/6). Split G's 3 parts(p) into 6 equal units(u). Do likewise for F as well. Then we can take away 1u from G, leaving 5u. Hence, the <After> model.


<After>

**<-------5u------>
E |--------------------|------|*******--> 5u + 320
F |---|---|---|---|---|---|---|---|*****--> 8u
G |---|---|---|---|---|<320>******--> 5u

Apply <Unchanged Total concept> to E,G, we have ...

<E+G Before> = <E+G After>

8u - 200 + 6u = 5u + 320 + 5u
14u - 200 = 10u + 320
14u - 10u --> 320 + 200
4u --> 520
1u --> 130

At end,
E = 5u + 320 --> (5 x 130) + 320 = 650 + 320 = 970
F = 8u --> 8 x 130 = 1040
G = 5u --> 5 x 130 = 650

E : F : G
970 : 1040 : 650
97 : 104 : 65

========================================

Trust the above helps.

Do let me know again should there be any clarification.

Cheers,
Edward

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