Subject: General Aptitude · Chapter: Time and Work · Exam: 2010 · Marks: · Difficulty:
Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need $4\frac{1}{2}$ hours more to complete the job than they both working together. What time would they take to do the work together ?
(a)4 hours
(b)5 hours
(c)6 hours
(d)7 hours
Answer
Answer (as printed): C
Explanation
Let A and B together take x hours to complete the work. Then, A alone takes (x + 8) hrs and B alone takes 9 x + hrs to complete the work. 2 1 1 1 Then, + = ( x + 8) 9 x x + 2 1 2 1 ⇒ + = ( x + 8) (2 x + 9) x ⇒ x (4x + 25) = (x + 8) (2x + 9) ⇒ 2x2 = 72 ⇒ x2 = 36 ⇒ x = 6.
Explanation as extracted from the printed page; notation may be imperfect.