[25 days] A can do a certain work in the same time in which B and C together can do it. If A and B together co

For Competitive Exams

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

15 days

20 days

25 days

30 days

Explanation:

$\left(A + B\right)$s 1 days work =$ \dfrac{1}{10} $

Cs 1 days work =$ \dfrac{1}{50} $

$\left(A + B + C\right)$s 1 days work =$ \left(\dfrac{1}{10} +\dfrac{1}{50} \right) $=$ \dfrac{6}{50} $=$ \dfrac{3}{25} $. .... [i]

As 1 days work = $\left(B + C\right)$s 1 days work .... [ii]

From [i] and [ii], we get: 2 $\times $[As 1 days work] =$ \dfrac{3}{25} $

$\Rightarrow$ As 1 days work =$ \dfrac{3}{50} $.

$\therefore$ Bs 1 days work$ \left(\dfrac{1}{10} -\dfrac{3}{50} \right) $=$ \dfrac{2}{50} $=$ \dfrac{1}{25} $.

So, B alone could do the work in 25 days.

Additional Questions

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