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25 May, 01:59

A quantity a varies inversely as a quantity b, if, when b changes a changes in the inverse ratio. What happens to the quantity a if the quantity b doubts?

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  1. 25 May, 02:42
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    quantity a is halfed

    Corrected question;

    A quantity a varies inversely as a quantity b, if, when b changes a changes in the inverse ratio. What happens to the quantity a if the quantity b doubles?

    Step-by-step explanation:

    Analysing the question;

    A quantity a varies inversely as a quantity b,

    a ∝ 1/b

    a = k/b ... 1

    when b changes a changes in the inverse ratio;

    Since the change at the same ratio but inversely, k = 1

    So, equation 1 becomes;

    a = 1/b

    If the quantity b doubles,

    ab = 1

    a1b1 = a2b2

    When b doubles, b2 = 2b1

    a1b1 = a2 (2b1)

    Making a2 the subject of formula;

    a2 = a1b1 / (2b1)

    a2 = a1/2

    Therefore, when b doubles, a will be divided by 2, that means a is halfed.
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