Subject

    Quantitative Aptitude

    Topic

    Time and Work

    Sanjay is twice as good a workman as his brother and together they finish a piece of work in 18 days. In how many days would Sanjay alone finish the work?

    ক)
    24 days
    খ)
    27 days
    গ)
    25 days
    ঘ)
    28 days
    ঙ)
    32 days

    Explanation

    Let’s assume that Sanjay alone finishes the work in ‘x’ days. ∴ Amount of work done by Sanjay in one day = 1/x Sanjay is twice good a workman as his brother ∴ No. of days taken by his brother to finish the same work would be 2x days. ⇒ Amount of work done by his brother in one day = 1/2x Since they together can finish the work in 18 days ∴18×[1x+12x]=1\therefore 18 \times \left[ {\frac{1}{x} + \frac{1}{{2x}}} \right] = 1 ⇒1x+12x=118\Rightarrow \frac{1}{x} + \frac{1}{{2x}} = \frac{1}{{18}} ⇒32x=118\Rightarrow \frac{3}{{2x}} = \frac{1}{{18}} ⇒ x = 27 ⇒ x = 27 days.
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