math

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my age now is one third of mum's age.8years ago,i was a fifth of mum's age was at that time.how old will my mother be 8 years from now

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    Let my age now be A, and let Mum's age now be M. Then we know that:
    A = M/3, so 3A = M
    A-8 = (M-8)/5, so 5A-40 = M-8
    but M = 3A, so 5A-40 = 3A-8
    so 2A = 40-8 = 32
    so A = 16
    so M = 48.
    Check it: A is one-third of M, and eight years ago I would have been 8 and Mum would have been 40.
    But I want to know what Mum's age will be 8 years from now, so that will be 48 + 8 = 56.

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