36. 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 1/2 hours more to complete the job than they both working together. what time would they take to do the work together?

A. 6 hours B. 4 hours C. 5 hours D. 7 hours

Answer Answer: Option A Explanation: Let A and B together take x hours to complete the work. then,
A alone takes (x+8) hrs and B alone takes (x + 9/2) hrs to complete the work. then,
1/(x+8) + 1/(x+9/2) = 1/x = 1(x+8)+ 2/(2x + 9) = 1/x = x(4x + 25) = (x+8) (2x+9)
= 2x^2 = 72 = x^2 =36 = x =6.

37. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

A. 60 days B. 30 days C. 40 days D. 70 days

Answer Answer: Option A Explanation: Let A's 1 day's work = x and B's 1 day's work =y.
Then, x+y = 1/30 and 16x + 44y =1.
Solving these two equations, we get : x = 1/60 and y = 1/60.
therefore B's 1 day's work = 1/60.
Hence, B alone shall finish the whole work in 60 days.

38. A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days, the work will be completed?

A. 7 1/3 days B. 8 1/5 days C. 10 1/4 days D. 5 1/2 days

Answer Answer: Option C Explanation: (A+B)'s 2 days' work = (1/9+1/12)= 7/36.
work done in 5 pairs of days = (5*7/36) = 35/36.
remaining work = (1- 35/36) = 1/36.
on 11th day, it is A's turn. 1/9 work is done by him in 1 day.
1/36 work is done by him in (9*1/36) = 1/4 day.
therefore total time taken = ( 10 + 1/4) days = 10 1/4 days.

39. A & B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days in how many days can B alone complete that work?

A. 7 days B. 5 days C. 6 days D. 9 days

Answer Answer: Option C Explanation: (A + B)'s 1 day's work = 1/4; A's 1 day's work = 1/12;
B's 1 day's work = (1/4 - 1/12) = 1/6
Hence B alone can complete the work in 6 days.

40. Ronald and elan are working on assignment. Ronald takes 6 hours to type 32 pages on a computer, while elan takes 5 hours to type 40 pages. how much time will they take, working together on two different computers to type an assignment of 110 pages?

A. 7 hours 30 minutes B. 8 hours C. 8 hours 15 minutes D. 8 hours 25 minutes

Answer Answer: Option C Explanation: Number of pages typed by Ronald in 1 hour = 32/6 = 16/3.
Number of pages typed by elan in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3.
therefore time taken by both to type 110 pages = (110*3/40) hrs = 8 hrs 15 min.