Question

A and B can separately do a piece of work in 20 and 15 days, respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in the next 4 days, then the number of days in which C alone could do the work will be

• A. 60 days
• B. 40 days
• C. 35 days
• D. 30 days

Answer 1

Answer: (B)

40 days

Answer 2

Work done by A in one day $=\frac{1}{20}$ and work done by B in one day $=\frac{1}{15}$

Work done by both A and B in one day $=\frac{1}{20}+\frac{1}{15}=\frac{7}{60}$

Work done by A and B in 6 days $=\frac{7}{60}$ × 6 $=\frac{7}{10}$

Remaining Work $=1-\frac{7}{10}=\frac{3}{10}$

Now, Time taken by A and B to complete the work in next 4 days is given by

⇒ (Remaining work / (A + C)'s effeciency) = Remaining time to complete the work.

⇒ $\frac{1}{20}+\frac{1}{C}=4 days$

⇒ $\frac{3}{10}=4(\frac{1}{20}+\frac{1}{C})$

⇒ $\frac{3}{10}=\frac{4}{20}+\frac{4}{C}$ ⇒ $\frac{4}{C}=\frac{3}{10}-\frac{1}{5}$

⇒ $\frac{1}{C}=\frac{1}{40}$ (or) C = 40 days

Hence, option B is the correct answer.The correct option is (B): 40 days