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.