Posted by Lance on Wednesday, October 24, 2012 at 4:35am.
Three boys shared some cards. Peter had twice as many cards as Farid. The ratio of the number of cards Peter had to the number of cards Kiran had was 6:5. Farid gave 2/3 of his cards to Peter and the rest to Kiran. How many cards did Kiran have at first if he received 10 cards from Faird.

Maths  Reiny, Wednesday, October 24, 2012 at 8:50am
Farid had x
Peter had 2x
Peter : Kiran = 2x : k = 6 : 5
2x/k = 6/5
6k = 10x
k = 5x/3
Kiran had 5x/3
Farid gives (2/3)(x) to Peter
Farid gives (1/3)(x) to Kiran
but this (1/3)x = 10
x=30
So...
Farid had 30
Peter had 60
Kiran had 50
check:
Peter had twice as many as Farid ✔
ratio of peter to Kiran = 60:50 = 6:5 ✔
Kiran got 10 cards from Farid, which should be (1/3)(30) ✔
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