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

Answer: (D)

$3\frac{3}{7}$ hours

Answer 2

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