Maths

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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 -

    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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