Question

B can do a piece of work in 6 hours, B and C together can do it in 4 hours, and A, B and C together \(2\frac{2}{3}\) hours. In how many hours can A and B together do the same piece of work?

• A. 11 hours
• B. \(6\frac{1}{7}\) hours
• C. \(2\frac{3}{7}\) hours
• D. \(3\frac{3}{7}\) hours

Answer 1

The Correct Option is D

Work done by B in one hour \(=\frac{1}{6}\)

Work done by B and C together in one hour \(=\frac{1}{B}+\frac{1}{C}=\frac{1}{6}+\frac{1}{12}=\frac{1}{12}\)

Work done by A, B and C together in one hour,

\(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{3}{8}\)

\(\frac{1}{A}+\frac{1}{6}+\frac{1}{12}=\frac{3}{8}\)

\(\frac{1}{A}=\frac{3}{8}-\frac{1}{6}-\frac{1}{12}\)

\(\frac{1}{A}=\frac{9-4-2}{24}=\frac{1}{8}\)

Work done by A and B together in one hour \(=\frac{1}{A}+\frac{1}{B}=\frac{1}{8}+\frac{1}{6}=\frac{7}{24}\)

Total work done by A and B together \(=\frac{24}{7}(or)3\frac{3}{7}\) hours

Hence, option D is the correct answer.The correct option is (D): \(3\frac{3}{7}\) hours