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.
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) ✔