Question

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together an do it in 2 hours. How long will B alone take to do it?

• A. 8 hours
• B. 20 hours
• C. 12 hours
• D. 24 hours
• E. 6 hours

Answer 1

The correct option is C

12 hours

A’s 1 hour’s work =$\frac{1}{4}$;

(B+C)’s 1 hour’s work = $\frac{1}{3}$;

(A+C)’s 1 hour’s work = $\frac{1}{2}$;

(A+B+C)’s 1 hours work = $(\frac{1}{4}+\frac{1}{3})=\frac{7}{12}$

B’s 1 hour’s work = $(\frac{7}{12}-\frac{1}{2})=\frac{1}{12}$

Therefore, B alone will take 12 hours to do the work.