TIME AND WORK

    Q1.  A set of cows can eat a crop in 20 days. However 10 cows did not go to the crop. The remaining now can eat in 25 days. Find the original number of cows

            (a)  45                        (b)  36   

            (c)  44                        (d)  50   

    Q2.  If 5 men or 10 women can do a job in 2 days, find how long 5 Men and 5 Women to do the same.

            (a)  1.2                       (b)  2     

            (c)  1.5                       (d)  1.6  

    Q3.  A can do work in 3 days less than B, A works alone for 4 days and than B takes over and completes it. If together 14 days were taken, how many days would each take to complete the work?

            (a)  11 and 14            (b)  8 and 11     

            (c)  15 and 18            (d)  12 and 15   

    Q4.  A and B have to make 600 machine parts, A worked for 2 hours and B for 5 Hours and they did half the entire work. They worked together for another three hours and found that 1/20th of the work is yet to be done. How much time does each take to do the whole work?

            (a)  11 and 14            (b)  8 and 11     

            (c)  15 and 18            (d)  12 and 15

    Q5.  A and B can mow the lawn in 6 hrs, B and C can mow the lawn in 8 hrs and A and C can mow the lawn in 10 hrs. How long will it take the lawn if all three work together?

            (a)  5.3                       (b)  5.1  

            (c)  5.2                       (d)  5.6  

    Q6.  A, B, C are three typists who can type 216 pages in 4 hrs. in one hr C types as many pages as B as B can type more than A. IN five hrs C can type as many pages as A in seven hrs. How many pages does each type in one hr.

            (a)  15, 18, 21            (b)  16, 19, 22

            (c)  12, 15, 18            (d)  18, 21, 24   

    Q7.  10 deer and 10 buffalos eat grass of 5 acres in a certain time. How many acres will feed 20 deer and 10 buffalos for the same time, supposing a buffalo eats as much as 2 deer?

            (a)  7.5                       (b)  6.67

            (c)  7                          (d)  6.95

    Q8.  A contractor undertook to do a certain work in 40 days and employed 60 men for it. In 15 days only 1/4th of the work was done. How many extra men should the contractor employ in order to complete the work in time?

            (a)  48                        (b)  50   

            (c)  40                        (d)  42   

    Q9.  A and B can do a piece of work in 20 and 25 days respectively. They started the work together and after some days A leaves the work and B completes the remaining work in 13 days. After how many days did A leave?

            (a)  6.66                     (b)  6     

            (c)  7.66                     (d)  7     

  Q10.  A cistern can be filled by one pipe A in 10 minutes, by a second pipe B in 25 minutes. It can be emptied by a waste pipe C in 10 minutes. In what time will the cistern be filled if all the three were turned on at once?

            (a)  25 min                 (b)  20 min        

            (c)  12 min                 (d)  30 min        

  Q11.  A chemical plant has 4 tanks A, B, C and D, each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:

            From A to B @ 20 litres/minute

            From C to A @ 90 litres/minute

            From A to D @ 10 litres/minute

            From C to D @ 50 litres/minute

            From B to C @ 100 litres/minute

            From D to B @ 110 litres/minute

            Which tank gets emptied first and how long does it take in minutes to get empty after pumping starts?

            (a)  A, 16.66               (b)  C, 20          

            (c)  D, 20                   (d)  D, 25          

  Q12.  In nuts and bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

            (a)  130 min               (b)  135 min      

            (c)  170 min               (d)  180 min      

  Q13.  It takes 6 technicians a total of 10 hours to build a new server from direct computer, with each working at the same rate. If six technicians start to build the server at 11:00 am and one technician per hour is added beginning 5:00 pm at what time will the server be complete?

            (a)  6:40 pm               (b)  7:00 pm      

            (c)  7:20 pm               (d)  8:00 pm      

  Q14.  3 small pumps and a large pump are filling a tank. Each of the three small pumps works at 2/3rd the rate of the large pump. If all 4 pumps work at the same time, they should fill the tank in what fraction of time that it would have taken the large pump alone?

            (a)  4/7                       (b)  1/3  

            (c)  1/3                       (d)  3/4  

  Q15.  Three friends’ asit, Arnold and afzal, work together to get all of these chores done. The time it takes them to do the work together is six hours less than asit would have taken working alone and half the time afzal would have taken working alone. How long did it take them to do these chores working together?

            (a)  20 min                 (b)  30 min        

            (c)  40 min                 (d)  50 min        

  Q16.  A takes 4 days to do a work. B takes twice as long as B and D takes twice as long as C. they are made in groups of two. One of the groups takes two third of the time taken by the second pair. What is the combination of the first pair?

            (a)  A, C                     (b)  A, D

            (c)  B, C                     (d)  B, D

Ans1.  (d)  Suppose number of cows = X

                  X can do the job in 20 days = 20X

                  Since 10 did not go, X – 10 could do the job in
25 days = (X – 10)25

                  Since job is same

                  20X = (X – 10)25

                  X = 50 cows

Ans2.  (d)  Here 5 men’s work = 10 women’s work

                  One man’s work = 5/10 = 1/2 women’s work

                  Therefore when it is 5 Men + 5 women

                  It is 5 men + 2.5 men = 7.5 men

                  Since 5 men can do the job in 2 days

                  1 man can do the job in 10 days

                  7.5 men can do the job in 12/7.5 = 1.6 days

Ans3.  (d)  Let B does the job in X days

                  Therefore A does the job in X – 3 days

                        As per problem 4/(X – 3) + 10/X = 1

                  Solving B’s days for job, X = 15, therefore A’s days = 15 – 3 = 12                     

Ans4.  (d)  Here suppose A does x machine parts per hour and B does y machine part per hour, therefore
2x + 5y = 300 and 3x + 3y = 270

                  Solving x = 50, so A can do in 12 hrs and y = 14, so y can do in 15 hrs

Ans5.  (b)  In one hour A and B can do 1/6th of lawn

                  In one hour B and C can do 1/8th of lawn

                        In one hour A and C can do 1/10th of lawn

                                           Adding the three   = 2(A + B + C)

                                           = 47/120  = (47/240) th of job

                        Reciprocating 240/47 = 5.1 days   

Ans6.  (a)  Let A types x pages per hour

                  B types y pages per hour

                                    C types z pages per hour

                  As per question, 4x + 4y + 4z        = 216

                                                 y – x = z        

                                                     5z = 7x

                  Three equations three variables, solving

x = 15, y = 18, z = 21

Ans7.  (b)  Since buffalos eat twice than deer, then 1 buffalo’s work = 2 deer work

                  So for first job, 10 deer and 10 buffalos = 15 buffalos

                  And fore second job, 20 deer and 10 buffalos = 20 buffalos

                  If 15 buffalos can eat 5 acres in certain time, then in same time 20 buffalos will eat

                                    20/15  × 5 = 6.67 acres

Ans8.  (a)  Work to be done in 40 days, as per schedule,
1/4th of the work done in 15 days therefore the total work will be done in 60 days. Now mandays required for the entire job are 60 × 60 = 3600. Mandays required for the left 3/4th of job = 3600 × ¾ = 2700

                        Mandays left with contractor

                                    = 25 × 60 = 1500

                        Excess mandays required

                                    = 2700 – 1500 = 1200

                        Here days cannot be extended therefore men required

                                    = 1200/25  = 48 men

Ans9.  (a)   Suppose A worked for X days

                  A can do the job in 20 days, in one day 1/20th of the job, in X days = X/20th of job

                  B can do the job in 25 days, in one day 1/25th of the job, in X + 10 days = X + 13/24th of job

                  Now since the job is done

                  X/20 + (X + 13)/25 = 1

                  Solving               X = 6.66 days

Ans10. (a)  In one minute the amount of filing =  1/10 + 1/25

                  In one minute the mount of emptying = 1/10

                  Net effect =  1/10 + 1/25- 1/10 = 1/25, the cistern will fill in 25 minutes

Ans11. (c)  Lets see the flow through the table below:

                                     – 20                 + 20

                                     + 90                                        – 90

                                     – 10                                                                 + 10

                                                                                    – 50                 + 50

                                                            – 100                + 100

                  D gets emptied first; it gets emptied in 20 minutes.

Ans12. (d)  Time taken in producing 9000 nuts

                  =  9000/100 × 1 + 9000/1000 × 5

                  =  90 + 45  =  135 minutes

                  Time taken in producing 9000 bolts

                  =  9000/75 × 1 + 9000/1500 × 10

                  = 120 + 60 =  180 minutes

                  Thus for making 9000 pairs of nuts and bolts time taken is 180 minutes.

Ans13. (d)  Time between 11 am to 5 pm  = 6 hours

                  Now , 6 technicians take 10 hours to build a new server from direct computer.

                  Thus 1 technician takes 10 × 6 = 60 hours

                  i.e. in 1/60 of new server is built by 1 technician in an hour.

                  6 technicians work for 6 hours

                  Thus wok done by them = 36/60 = 3/5

                  Remaining work = 1 –  3/5 = 2/5

                  Now , 7 technicians work from 5 pm to 6 pm

                  Thus work done by them = 7/60

                  Again, 8 technicians work from 6 pm to 7 pm

                  Thus work done by them = 8/60

                  Again, 9 technicians work from 7 pm to 8 pm

                  Thus work done by them = 9/60

                  Thus total work done        =  7/60 + 8/60 + 9/60

                                                  = 24/60 = 2/5

                  Hence, the server is built at 8 pm.

Ans14. (b)  Let the rate of large pump be x units/hr

                  So rate of each small pump  = 2x/3

                  When 4 pumps work at the same time, their combined rate = 3 × 2x/ 3 + x = 3x

                  Time taken = 1/3 of time taken be the large pump

Ans15. (c)  40 min

Ans16. (b)  A’s 1 day’s work  = ¼

                  By hypothesis,

                  B’s 1 day’s work  =  1/8

                  C’s 1 day’s work  =  1/16

                  D’s 1 day’s work  =  1/32

                  Thus  (A + D)’s 1 day’s work

                                    =  ¼ + 1/32 = 9/32

                  And (B + C)’s 1 day’s work

                                    = 1/8 + 1/16 =  3/16

                  (B + C) can finish the work in 16/3 days

                  Thus (A + D) can finish the work in

                                    = 32/9 days

                                                = 2/3 × 16/3

                                    = 2/3rd of time taken by B and C