Aptitude Time And WorkPage 4
25. | | A, B and C can complete a piece of work in 9, 12 and 18 days respectively. In how much time can A and C together complete a work, which B alone can complete in 48 days? | | (a)24 days | | (b)96 days | | (c)36 days | | (d)72 days |
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Answer is: AGiven, A, B and C together can complete a piece of work in 9, 12 and 18 days.
The work done by A and C in one day = 1/9 + 1/18 = 1/6th of the work.
so, it takes A and C together 6 days to complete a piece of work for which B takes 12 days to complete.
A and C together take half of the time taken by B.
therefore, If B takes 48 days to complete a work , A and C together take 24 days.
26. | | P and Q are 300 km apart. At 8:00 am, Buses X and Y left P and Q simultaneously for Q and P respectively. If the speeds of buses X and Y are 40 kmph and 60 kmph respectively, when do they meet? | | (a)10:00 am | | (b)11:00 am | | (c)12:00 pm | | (d)10:30 pm |
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Answer is: BThe relative speed = (40 + 60) = 100 kmph
Therefore, time taken for them to meet = 300/100 = 3 hours
8:00 am + 3 hours = 11:00 am.
27. | | A and 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 can complete the work? | | (a)8 days | | (b)7 days | | (c)6 days | | (d)5 days |
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Answer is: C(A + B)'s 1 day's work = 1/4
A's 1 day's work = 1/12
So, B's 1 day's work = (1/4 - 1/12) = 1/6
Hence, B alone can complete the work in 6 days.
28. | | A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work? | | (a)18 days | | (b)27 days | | (c)36 days | | (d)32 days |
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Answer is: B(A's 1 day 's work) : (B's 1 day 's work) = 2 : 1
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the ratio 2 : 1
So, A's 1 day's work = (1/18) X (2/3) = 1/27.
Hence, A alone can finish the work in 27 days
29. | | A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone? | | (a)13/2 days | | (b)7 days | | (c)15/2 days | | (d)8 days |
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Answer is: CSon's 1 day's work = (1/3 - 1/5) = 2/15.
Hence, the son alone can do the work in 15/2 days.
30. | | A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? | | (a)5 | | (b)4 | | (c)6 | | (d)8 |
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Answer is: CB's 10 day's work = 1/15 X 10 = 2/3.
Remaining work = (1 - 2/3) = 1/3.
Now, 1/18 work is done by A in 1 day.
So, 1/3 work is done by A in 18 X 1/3 = 6 days.
31. | | P and Q can do a piece of work in 20 days and 12 days respectively. P started the work alone and then after 4 days Q joined him till the completion of the work. How long did the work last? | | (a)6 days | | (b)10 days | | (c)15 days | | (d)20 days |
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Answer is: BWork done by P in 4 days = 1/20 X 4 = 1/5.
Remaining work (1 - 1/5) = 4/5.
(P + Q)'s 1 day's work = (1/20 + 1/12) = 2/15.
So, 4/5 work will is done by P and Q in (15/2) X (4/5) = 6 days.
Hence, total time taken = 6 + 4 = 10 days
32. | | 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)30 days | | (b)40 days | | (c)60 days | | (d)70 days |
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Answer is: CLet A's 1 day's work = x
B's 1 day's work = y
Then, x + y = 1/30
And 16x + 44y = 1
Solving these equations, we get, x = 1/60, y = 1/60
So, B's 1 day's work = 1/60
Hence, B alone shall finish the whole work in 60 days
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