21. A can do 3/4 of a work in 12 days in how many days can he finish 1/8 of the work ?
(a)8 (b)12
(c) 7 (d) 2
Answer: (d) 2
Solution:
Let it takes A, D days to complete the work. Then,
(3/4)D = 12
=>D=12x(4/3) = 16 days
Then 1/8 of the work would be done in = (1/8)x 16 = 2 days.
22. A man ,a woman or a boy can do a job in 20 days ,30 days or 60 days respectively. How many boys must assist 2 men and 8 women to do the work in 2 days ?
(a) 18 (b) 8
(c) 10 (d) 14
Answer: (b) 8
Solution:
Work done by a boy in one day = 1/60
Work done by a woman in one day = 1/30
Work done by a man in one day = 1/20
Now, Work done by 2 men and 8 women in one day = (2/20 + 8/30) = (6+16)/(60) = 22/60
And in two days they would be completed 2 x (22/60) = 44/60
Now, Work remaining = 1 - 44/60 = 16/60
Since, A boy does 1/60 of the work in day. Therefore, Number of employed to do the work
= 16/60/1/60 = 16 boy-day in 2 days and 8 boys in one day.
23. A and B working alone can finish a job in 5 days and 7 days respectively.They work at it alternately for a day. If A starts the work, find in how many days the job will be finished ?
(a) 29/5 (b) 11/5
(c) 24/5 (d) 21/5
Answer: (a) 29/5
Solution:
Work done by A in one day = 1/5
and work done by B in one day = 1/7
They are working alternately.
Therefore, Work done in first two day = (1/5 + 1/7) = 12/35
Work done in first four day = 24/35
Work done in first 5 days = 24/35 + 1/5 = 31/35
Remaining work = 4/35
Day it will take B to complete = 4/35/1/7 = 4/5 of the day.
Therefore Total days taken = 5 + 4/5 = 29/5 days
24. A can complete a work in 25 days and B can do the same work in 10 days. If A after doing 4 days leaves the work. Find in how many days B will do the remaining work ?
(a) 42/5 (b) 22/5
(c) 11/5 (d) 32/5
Answer; (a) 42/5
Solution:
Work done by A in ` day = 1/25
And work done in 4 days = 4/25
Remaining work = 21/25
Since, Work done by B in 1 day = 1/10
Days it will take B to complete the work = 21/25/1/10 = 42/5
25. A can do a piece of a work in 12 days. A does the work for 2 days and leaves the job.B does the remaining work in 5 days. In how many days B alone can do the work ?
(a) 16 (b) 18
(c) 20 (d) 6
Answer: (d) 6
Solution:
Work done in 1 day by A = 1/12.
He worked for 2 days and completed 2/12 = 1/6 of the work.
Remaining work = 5/6 and completed by B in 5 days.
Therefore , Work done by B in 1 day = 5/6/5 = 5/30 or 1/6
And total work would have been done by B alone = 1/1/6 = 6 days.
26. A can do a piece of work in 80 days.He works at it for 10 days and than B alone finishes the remaining work in 42 days. In how much time will A and B working together finish the work ?
(a) 10 (b) 5
(c) 25 (d) 30
Answer: (d) 30
Solution:
Work Done by A in 1 day = 1/80
And work done in 10 days = 10/80 = 1/8
Work left = 1 - 1/8 = 7/8
It was completed in 42 day.
Therefore Work done by B in 1 day = 7/8/42 = 1/48
And Days it will take B to complete the work = 1/1/48 = 48 days.
And A and B working together = 48x80/(48 + 80) = 3840/128 = 30 days.
27. After A has completed 1/3 rd of piece of work in 4 days, B completes the rest of it in 16 days.In how many days can A and B complete the work together ?
(a) 8 (b) 10
(c) 12 (d) 13 (e) none of these
Answer: (a) 8
Solution:
Work Done by A =1/3 and days it took to complete 1/3 of the work = 4
Therefore, Work done by A in 1 day = 1/3/4 = 1/12
And Total days A would have taken to finish the work = 1/1/12 = 12 days.
Work done by B= 2/3 and it took him 16 days
Therefore, work done per day by b = 2/3/16 = 1/24
And it would take him 1/1/24 = 24 days to finish it alone.
Using the formula when two are working together = 24x12/(24 + 12) = 8 days
28. 20 men can prepare 40 toys in 24 days working 18 hours a day then in how many days can 36 men prepare 48 toys working 16 hrs a day ?
(a) 16 days (b) 12 days
(c) 21 days (d) 18 days (e) none of these
Answer: (d) 18 days
Solution:
Using the formula, M1D1H1W2 = M2D2H2W1
We have , 20x24x18x48 = 36x16xD2x40
On solving for D2
D2 = 20x24x18x48/36x16x40 = 18 days
29. P can do a piece of work in 9 days. Q is 50% more efficient than P. The number of days it takes for Q to do the same piece of work is
(a) 4(1/2) (b) 6
(c) 3 (d) 13(1/2)
Answer: (b) 6
Solution:
Using the formula, E2D1= E1D2
=> (1)9 =(1.5)(D2)
=> D2 = 9/1.5
= 6
30. B and C can complete a piece of work in 12 days, C and A can do it in 8 days. All the three can do it in 6 days. A and B together can complete it in
(a) 4 days (b) 6 days
(c) 8 days (d) 10 days
Answer:
Solution:
Using the Formula mentioned in the List of Short-cut formula, we have
Number of days, A can do the work = (12x6)/(12-6) = 72/6 = 12 days
Number of days, B can do the work = (8x6)/(8-6) =48/2 = 24 days
Therefore, number of days A and B can do the work = (24)(12)/(24 + 12)
= 8 days
31. If 12 men or 24 boys can do a work in 66 days , the number of days in which 15 men and 6 boys can do it is
(a) 44 (b) 33
(c) 55 (d) 66
Answer:
Solution:
Since 12 men or 24 boys can do the same job in 66 days,
therefore the efficiency of a men to boy = 24/12 = 2/1
or men/boy = 2/1 => men = 2 boy
Therefore,15 men and 6 boys = 15 men + 6 (1/2)men = 15 +3 men = 18 men
Thus,
And number of days, 18 men can do the job
=> days = (12)(66)/(18) = 44 days
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