Subject: General Aptitude · Chapter: Time and Work · Exam: 2005 · Marks: · Difficulty:
A can do a piece of work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it?
(a)8 hours
(b)10 hours
(c)12 hours
(d)24 hours
Answer
Answer (as printed): C
Explanation
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 hour's work $= \frac{1}{4}+\frac{1}{3} = \frac{7}{12}$. $\therefore$ B's 1 hour's work = (A+B+C)'s 1 hour's work $-$ (A+C)'s 1 hour's work $= \frac{7}{12} - \frac{1}{2} = \frac{1}{12}$. So, B alone can complete the work in 12 hours.
Explanation as extracted from the printed page; notation may be imperfect.