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29 April, 07:59

Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and / small / frac{1}{7} of the remaining shares are shares of Company Y stock. How many shares of Company X stock does the investor own?

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  1. 29 April, 08:03
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    The question is not complete, find below the complete question:

    Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and 1/7 of the remaining shares are shares of Company Y stock. How many shares of Company X stock does the investor own?

    (1) The investor owns 100 shares of Company Y stock.

    (2) The investor owns 200 more shares of Company X stock than of Company Y stock

    1. X is 300 shares

    2. X is 300 shares

    Explanation:

    Going by the fact that the investor has a portfolio containing three companies' shares, the shares owned in company X can ascertained as follows:

    In the first instance, the investor had 100 shares of company Y:

    the shares in company Y is 1/7 after 30% held in company X has been deducted, i. e 1/7 * (1-30%) = 1/7*0.7=0.1

    0.1 is 10%, the shares in company Y is 10% of the entire portfolio

    The entire portfolio is = 100/0.1=1000 shares

    Number of shares held in company X = 1000*30%=300 shares

    In the second instance:

    The investor had 200 more shares in X than Y, which can be interpreted mathematically thus:

    0.3*entire portfolio-200 shares=0.1*entire portfolio

    let entire portfolio be P

    0.3P-200 shares=0.1P

    0.3P-0.1P=200 shares

    0.2P = 200 shares

    P=200 Shares/0.2

    P=1000 shares

    X is 30% of P=1000*30%=300 shares
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