CAT Question Bank  Time & Work

Q13) A water tank has three taps A, B and C. A fills 4 buckets in 24 min, B fills 8 buckets in 1 h and C fills 2 buckets in 20 min. If all the taps are opened together, a full tank is emptied in 2 h. If a bucket contains 5L water. What is the capacity of the tank ?

Q14) A tap can fill a tank in 25 min and another can empty it in 50 min. Find whether the tank will be filled up or emptied and in how many minutes ?

Q15) A pipe can fill a tank in 6 h. Due to leak in the bottom it is filled in 8 h. If the tank is full, how much time will the leak take to empty it ?

Q16) Two pipes A and B can fill a cistern in 24 min and 30 min respectively. There is also an outlet C. If all the three pipes are opened together, the tank is full in 20 min. How much time will be taken by C to empty the full tank ?

Q17) A cistern can be filled by two pipes in 30 and 40 min respectively. Both the pipes were opened at once, when the first pipe must be turned of so that may be just filled in 18 min.

Q18) One filling pipe ‘A’ is 6 times faster than second filling pipe B. If B can fill a cistern in 28 min, then find the time when the cistern will be full if both the pipes are opened together

Q19) Two pipes can fill a cistern in 30 and 15 h respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 5 h extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ?

Q20) Two pipes A and B can fill a cistern in 12 min and 16 min respectively. Both the pipes are opened together for a certain time but due to some obstruction the flow of water was restricted to 7/8 of full flow in pipe A and 5/6 of full in pipe B. This obstruction is removed after some time and the tank is now filled in 3 min from that moment. How long was it before the full flow began ?

Q21) Arvind and Swarnali are team mates and they can do a project in certain number of days.If Arvind is on holiday for x days,then they take y more days to complete the work while if Swarnali is on holiday for x days,then they take z more days to complete the same project. Then
(a) y, x/2,z are in AP
(b) y, x/2,z are in GP
(c) 1/x=1/y+1/z
(d) Cannot be determined
(e) None of the foregoing

Q22) Sunit,Arun and Pavan were in the same project for 30 days. In the course of work all of them remained absent for few days.Pavan remained 10 days more absent than Arun remained and Sunit did onethird of the total work.How many more days did Pavan remained absent than Sunit?
(a) 4
(b) 5
(c) 6
(d) Cannot be determined
(e) None of the foregoing

Q23) Divya and Raveena can do a work alone exactly in 20 and 25 days respectively. However, when they work together, they do 25% more work than is expected. If they work for a few days alone and for few days together (both being integers only), then the work could not have been completed in exactly
(1) 10 days
(2) 14 days
(3) 16 days
(4) 17 days
(5) either none or atleast 2 of these

Q24) Sara, Kyna, Riddhi can complete the work W1, W2, W3 alone in 6, 9 and 15 days respectively. If (Kyna, Riddhi), (Riddhi, Sara) and (Sara, Kyna) can do the work W1, W2, W3 respectively in n days each, then n lies in
(1) (3, 3.5)
(2) (3.5, 4)
(3) (4, 4.5)
(4) (4.5, 5)
(5) either none or atleast 2 of these

Q25) A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In how many days C alone will do the work?
(a) 16
(b) 36
(c) 24
(d) 48

Q26) Divya works for Google that claims only 4 working days. In the 1st week of joining, she went for movies after 4 working days. On Friday, she noticed that the fraction p of the line is in front of her, while 1/q of the line was behind her. On Saturday, the same fraction p of the line was in front of her, while 1/(q+1) of the line was behind her. On Sunday, the same fraction p of the line was in front of her, while 1/(q+2) of the line was behind her. For how many values of p is this possible?
(a) 3
(b) 1
(c) 2
(d) no such value
(e) infinitely many

Q27) can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the work was
(a) 12 and half days
(b) 15 days
(c) 14 and 2/9 days
(d) 16 and 2/3 days

Q28) A, B and C can do a work together in a certain number of days. If A leaves after half the work is done, then the work takes 4 more days for completion, but if B leaves after half the work is done, the work takes 5 more days for completion. If A takes 10 more days than B to do the work alone, then in how many days can C alone do the work?
(a) 45
(b) 52.5
(c) 60
(d) 65
(e) none of the foregoing

Q29) The painting of a hotel can be done by 10 painters in 5 days. But, in reality there were few dabblers in the group of 10 painters and therefore the work took a little over 6 days for completion. A painter worked twice as fast as the dabbler and used 25% less paint than a dabbler used. If 5 litres extra paint was used than expected, then the total paint used in painting the hotel was (in litres)

Q30) A, B and C can do apiece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days ?
(a) 1 day
(b) 9 days
(c) 8 days
(d) 10 days

Work done by all machines working together = (1/3 + 1/4 + 1/6) = 9/12 = 3/4th of work
Hence required number of days to complete the job = 4/3 days

Let there were x men in the grop who decided to complete the job in 8 days.
Since, 10 men dropped out every day, the number of men who worked all the 12 days
= x + (x – 10) + (x – 20) + .... + (x – 110)
= 12x  11/2 [2 * 10 + (11  1) * 10]
= 12x  660avg = (12x  660)/12 = (x  55) men per day
job took 3/2 time more the normal time (from 8 days to 12 days)
(x  55) = x * 2/3 => x = 165 men.