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At ' t' minute past 2pm,the …

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At ' t' minute past 2pm,the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t2÷4 minutes .find value of ''t''.

    • Posted by Rahul Kumar 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Since, there are 60 minutes gap between 2 PM & 3 PM.
    Time needed by minutes hand after t minutes past 2 PM to show 3 PM = (60 - t) minutes
    According to the question ;
    60 - t = {tex}\frac{t^2}{4}{/tex} - 3
    {tex}\Rightarrow{/tex} 63 = {tex}\frac{t^2}{4}{/tex} + t
    {tex}\Rightarrow{/tex} 63 = {tex}\frac{t^2 + 4t}{4}{/tex}
    {tex}\Rightarrow{/tex} 252 = t2 + 4t
    {tex}\Rightarrow{/tex} t2 + 4t - 252 = 0
    {tex}\Rightarrow{/tex} t2 + 18t - 14t - 252 = 0
    {tex}\Rightarrow{/tex} t(t + 18) - 14(t + 8) = 0
    {tex}\Rightarrow{/tex} (t + 18)(t - 14) = 0
    {tex}\Rightarrow{/tex}  t + 18 = 0 or t - 14 = 0
    {tex}\Rightarrow{/tex} t = -18 or t = 14
    Since time cannot be negative, t {tex}\neq{/tex} -18
    Hence, t = 14 minutes.

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