Wednesday, June 4, 2014

Solution to time Time and Work( 21- 29+)


  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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