32. A can do a piece of work in 80 days.He works at it for 10 days and then B alone finishes the remaining work in 42 days.In how much time will A and B working together finish the work?

A. 25 days B. 30 days C. 32 days D. 26 days

Answer Answer: Option B Explanation: Work done by A in 10 days = (1/80 * 10) =1/8
Remaining work = (1- 1/8) = 7/8
Now 7/8 work is done by B in 42 days
Whole work will be done by B in (42*8/7) = 48 days
A's 1 day's work = 1/80 and B's 1 day's work = 1/48
(A+B)'s 1 day's work = (1/80 + 1/48) = 8/240 = 1/30
Hence both will finish the work in 30 days.

33. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

A. 8 hours B. 12 hours C. 10 hours D. 24 hours

Answer Answer: Option B Explanation: A's 1 hour's work = 1/4; (B+C)'s 1 hour's work = 1/3; (A+C)'s 1 hour's work = 1/2.
(A+B+C)'s work = (1/4+1/3) = 7/12.
B's 1 hour's work = (7/12 - 1/2) = 1/12.
therefore B alone will take 12 hours to do the work.

34. A can do a piece of work in 20 days. B is 25% more efficient than A. The number of days taken by B to do the same piece of work is

A. 15 B. 16 C. 18 D. 25

Answer Answer: Option B Explanation: Ratio of times taken by A and B = 125 : 100 = 5 :4.
suppose B takes x days to do the work.
5 : 4 : : 20 : x = x = (4 *20/ 5) = x = 16 days.
hence B takes 16 days to complete the work

35. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in

A. 15 days B. 20 days C. 25 days D. 30 days

Answer Answer: Option C Explanation: (A+B)'s 1 day's work = 1/10; C's 1 day's work = 1/50.
(A+B+C)'s 1 day's work = (1/10+ 1/50) = 6/50 = 3/25
Also, A's 1 day's work = (B+C)'s 1 day's work
From(1)and (2) we get : 2* (A's 1 day's work) = 3/25.
= A's 1 day's work = 3/50.
therefore B's 1 day's work = (1/10 - 3/50) = 2/50 = 1/25.
so, B alone could do the work in 25 days.