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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