maths

A man has certain number of oranges.he divides them into two lotsA and B.he sells the first lot at the rate of Rs.2 for three oranges and the second lot at the rate of Re.1 per orange and gets a total of Rs.400.if he had sold the first lot at the rate of Re.1 per orange and the second lot at the rate of Rs.4 for 5 oranges,his total collection would have been Rs.460.Find the total number of oranges he had.

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  1. number in lot A ---- x
    number in lot b ---- y

    (2/3)x + y = 400
    times 3
    2x + 3y = 1200 **

    x + (4/5)y = 460
    times 5
    5x + 4y = 2300 ***

    ** times 4 : ---> 8x + 12y = 4800
    *** times 3: --> 15x + 12y = 6900
    subtract them:
    7x = 2100
    x = 300
    in **
    600 + 3y = 1200
    y = 200

    total is 500 oranges.

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