A can do 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:

Correct option is D

Given:

(A + B)'s 1 day's work = $$\frac{1}{10}$$
C 's 1 day's work = $$\frac{1}{50}$$​

Formula Used: 

Solution:

(A + B)'s 1 day's work = $$\frac{1}{10}$$​​
C 's 1 day's work = $$\frac{1}{50}$$​​
(A + B + C) 's 1 day's work = $$\frac{1}{10} + \frac{1}{50} = \frac{6}{50} = \frac{3}{25} \quad \text{.... (i)}$$​​
A's 1 day's work = (B + C)'s 1 day's work$$\quad \text{.... (ii)}$$​​
\text{From (i) and (ii) we get:}
​$$2 \times \text{(A's 1 day's work)} = \frac{3}{25}$$​​
​$$A \text{'s 1 day's work} = \frac{3}{50}\\B \text{'s 1 day's work} = \frac{1}{10} - \frac{3}{50} = \frac{1}{25}\\\text{So B alone could do the work in 25 days.}\\$$​​