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    Subject

    Quantitative Aptitude

    Topic

    Time and Work

    A takes twice as long as B and C together take to do a piece of work and B takes thrice as long as A and C together. However, the 3 men together can complete the work in 60 days. How long would C alone take to do the work?

    ক)
    180 days
    খ)
    144 days
    গ)
    140 days
    ঘ)
    250 days
    ঙ)
    90 days

    Explanation

    Let’s assume that A, B and C can individually finish the work alone in a, b and c days respectively. ∴ Part of work finished by A in one day = 1/a ∴ Part of work finished by A in one day = 1/b ∴ Part of work finished by A in one day = 1/c Now, as per the given information – A takes twice as long as B and C together ⇒ A does half the work of B and C together in equal time. ⇒1a=12×(1b+1c)\Rightarrow \frac{1}{a} = \frac{1}{2} \times \left( {\frac{1}{b} + \frac{1}{c}} \right) ⇒2a=1b+1c\Rightarrow \frac{2}{a} = \frac{1}{b} + \frac{1}{c}    -----(i) Similarly, B takes thrice as long as A and C together ⇒ B does 1/3 of (A & C) in equal time ⇒1b=13×(1a+1c)\Rightarrow \frac{1}{b} = \frac{1}{3} \times \left( {\frac{1}{a} + \frac{1}{c}} \right) ⇒3b=1a+1c\Rightarrow \frac{3}{b} = \frac{1}{a} + \frac{1}{c}      -----(ii) Also, A, B, and C together can complete the work in 60 days. ∴1a+1b+1c=160\therefore \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{{60}} ------(iii) Putting the value of (i) into (iii), we get, ⇒1a  +2a  =160⇒3A=160⇒1A=1180\begin{array}{l} \Rightarrow \frac{1}{a}\; + \frac{2}{a}\; = \frac{1}{{60}}\\ \Rightarrow \frac{3}{A} = \frac{1}{{60}}\\ \Rightarrow \frac{1}{A} = \frac{1}{{180}} \end{array} ∴ A takes 180 days to complete the entire work alone. 2a−1b=3b−1a⇒3a=4b\begin{array}{l} \frac{2}{a} - \frac{1}{b} = \frac{3}{b} - \frac{1}{a}\\ \Rightarrow \frac{3}{a} = \frac{4}{b} \end{array} ⇒ b = (4 × 180)/3 = 240 ∴ B takes 240 days to complete the entire work alone. Now, putting value of a and b in equation (iii) we get, ⇒  1180  +  1240  +  1c  =  160⇒  1C  =  160  −−  (1180  +  1240)⇒  1C  =  1144\begin{array}{l} \Rightarrow \;\frac{1}{{180}}\; + \;\frac{1}{{240}}\; + \;\frac{1}{c}\; = \;\frac{1}{{60}}\\ \Rightarrow \;\frac{1}{C}\; = \;\frac{1}{{60}}\;--\;\left( {\frac{1}{{180}}\; + \;\frac{1}{{240}}} \right)\\ \Rightarrow \;\frac{1}{C}\; = \;\frac{1}{{144}} \end{array} Hence, C takes 144 days to complete the entire work alone.

    Related questions

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