Question

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:

• A. 15 days
• B. 20 days
• C. 25 days
• D. 30 days
• E. 35 days

Answer 1

The correct option is C

25 days

(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 =$(\frac{1}{10}+\frac{1}{50})=\frac{6}{50}=\frac{3}{25}$ ……… (i)

Also, A’s 1 day’s work = (B+C)’s 1 day’s work

From (i) and (ii), we get: 2 × (A’s 1 day’s work) = $\frac{3}{25}$

⇒ A’s 1 day’s work = $\frac{3}{50}$;

∴ B’s 1 day’s work =$(\frac{1}{10}-\frac{3}{50})=\frac{2}{50}=\frac{1}{25}$

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