Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
A and B can finish a work, working on alternate days, in 19 days, when A works on the first day. However, they can finish the work, working on alternate days, in $19 \frac{5}{6}$ days, when B works on the first day. How many days does A alone take to finish the work?
(a)$11 \frac{1}{2}$ days
(b)15 days
(c)18 days
(d)21 days
Answer
Answer (as printed): A
Explanation
Let the time taken by A alone and B alone to complete the work be x days and y days respectively. When A works on the first day: 551 In this case, A works for 10 days while B works for 9 days. 10 9 \ + =1 ...(i) x y When B works on the first day: 5 59 In this case, A works for 9 days = days while B 6 6 works for 10 days. 59 10 \ + =1 ...(ii) 6x y Multiplying (i) by 10 and (ii) by 9 and then subtracting, 23 1 we get: x = = 11 . 2 2 1 Hence, A alone takes 11 days to complete the work. 2 1 1 7
Explanation as extracted from the printed page; notation may be imperfect.