Subject

    Quantitative Aptitude

    Topic

    Percentage

    In the expression ab2, the values of both variables a and b are decreased by 20%. By this, the value of the expression is decreased by

    ক)
    40%
    খ)
    80%
    গ)
    48.8%
    ঘ)
    51.2%
    ঙ)
    52.3%

    Explanation

    The given expression is ab2. Given that, value of both expression is decreased by 20%, then On decreasing a by 20% ⇒ new a = a – a × (20/100) = a – (a/5) = 4a/5 Similarly, new b = 4b/5 So now, expression ab2 will become (4a5)(4b5)2=64125ab2\left( {\frac{{4a}}{5}} \right){\left( {\frac{{4b}}{5}} \right)^2} = \frac{{64}}{{125}}a{b^2} Change in the value of expression = new expression – old expression ⇒ Change in the value of expression = ab2−64125ab2=61125ab2a{b^2} - \frac{{64}}{{125}}a{b^2} = \frac{{61}}{{125}}a{b^2} % decrease in the given expression = (change in expression)/(old expression) × 100 % decrease in the given expression =61125ab2ab2×100=61125×100=48.8%  = \frac{{\frac{{61}}{{125}}a{b^2}}}{{a{b^2}}} \times 100 = \frac{{61}}{{125}} \times 100 = 48.8\% \;

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