Question

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.

Answer 1

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) ✔