Subject: General Aptitude · Chapter: Time and Work · Exam: 2010 · Marks: · Difficulty:
Three friends Anne, Bob and Chris work together to do a certain job. The time it takes them to do the work together is 6 hours less than Anne would have taken alone, 1 hour less than Bob would have taken alone and half the time Chris would have taken working alone. How long did it take them to complete the job, working together?
(a)20 min
(b)30 min
(c)40 min
(d)50 min
Answer
Answer (as printed): C
Explanation
Let the time taken by the three friends together to do the work be x hours. Then, time taken by Anne alone = (x + 6) hrs; time taken by Bob alone = (x + 1) hrs; time taken by Chris alone = 2x hrs. 1 1 1 1 \ + + = x + 6 x + 1 2x x 2 x ( x + 1) + 2 x ( x + 6) + ( x + 1) ( x + 6) 1 ⇒ = 2 x ( x + 6) ( x + 1) x ⇒ 5x2 + 21x + 6 = 2(x2 + 7x + 6) ⇒ 3x2 + 7x – 6 = 0 ⇒ (x + 3) (3x – 2) = 0 ⇒ x = [Q 2 2 \ Required time = hrs = × 60 min = 40 min. 3 3
Explanation as extracted from the printed page; notation may be imperfect.