26. Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in?

A. 5 1/4 days B. 6 1/4 days C. 7 1/2 days D. none of these

Answer Answer: Option B Explanation: Let A's 1 day's work = x and B's 1 day's work = y.
Then, x+ y = 1/5 and 2x + 1/3y = 1/3.
solving, we get : x = 4/25 and y = 1/25.
therefore A's 1 day's work = 4/25.
so, A alone could complete the work in 25/4 = 6 1/4 days.

27. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

A. 5 6/11 B. 6 5/11 C. 5 5/11 D. 6 6/11

Answer Answer: Option C Explanation: P can complete the work in (12*8) hrs. = 96 hrs. Q can complete the work in (8*10) hrs. = 80 hrs.
therefore P's 1 hour's work = 1/96 and Q' s 1 hour's work = 1/80.
(P + Q)'s 1 hour' s work = ( 1/96 + 1/80) = 11/480.
so both P and Q will finish the work in (480/ 11) hrs.
therefore number of days of 8 hours each = (480/11*1/8) = 60/11 days = 5 5/11 days.

28. A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work?

A. 5 days B. 6 days C. 8 days D. 9 days

Answer Answer: Option B Explanation: A's 1 day's work = 1/10 and B's 1 day's work = 1/15.
therefore (A+B)'s 1 day's work =( 1/10+ 1/15)= 1/6.
so, both together will finish the work in 6 days.

29. 45 men can complete a work in 16 days. Six days after they started working 30 more men joined them.How many days will they now take to complete the remaining work?

A. 5 days B. 7 days C. 8 days D. 6 days

Answer Answer: Option D Explanation: (45*16) men can complete a work in 1 day
1 man's 1 day's work = 1/720
45 men's 6 day's work =(1/16*6) = 3/8, Remaining work = ( 1- 3/8) = 5/8
75 men's 1 day's work = 75/720 = 5/48
Now 5/48 work is done by them in 1 day
5/8 work is done by them in(48/5*5/8) = 6 days

30. A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. If A, B and C work together, they will complete the work in

A. 5 days B. 7 5/6 days C. 10 days D. 15 2/3 days

Answer Answer: Option C Explanation: (A+B)' s 1 day's work = 1/12; (B+C)'s 1 day's work = 1/ 15; (A+ C)'s 1 day's work = 1/20.
Adding, we get : 2 (A+B+C)'s 1 day's work = (1/12+1/15+1/20) = 12/60 = 1/5.
therefore (A+B+C)'s 1 day's work = 1/10.
so A,B and C together can complete the work in 10 days.