[12 hours] A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together c

For Competitive Exams

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

8 hours

10 hours

12 hours

24 hours

Explanation:

As 1 hours work =$ \dfrac{1}{4} $;

$\left(B + C\right)$s 1 hours work =$ \dfrac{1}{3} $;

$\left(A + C\right)$s 1 hours work =$ \dfrac{1}{2} $.

$\left(A + B + C\right)$s 1 hours work =$ \left(\dfrac{1}{4} +\dfrac{1}{3} \right) $=$ \dfrac{7}{12} $.

Bs 1 hours work =$ \left(\dfrac{7}{12} -\dfrac{1}{2} \right) $=$ \dfrac{1}{12} $.

B alone will take 12 hours to do the work.

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