## Time and Work Practice Problems Set - 1

Time and Work Practice Problems Set – 1
1. An inlet pipe fills a tank of capacity 1400 m3 at the rate of 200 m3/min. When an outlet pipe is also opened, the tank gets filled in 20 minutes. Find the time (in minutes) in which the outlet pipe empties a completely filled tank, if the inlet pipe is not open.
a) 7.77 min
b) 7 min
c) 70 min
d) 10 10/13 min
e) 11 10/13 min
2. A man is thrice as efficient as a woman and a woman is twice as efficient as a child. If all of them, working together, complete a task in 6 days, then find the number of days that the child will take to complete the task alone.
a) 9
b) 18
c) 36
d) 54
e) 45
3. Two workers are filling a drum with sand and one worker is emptying it. If the two workers can fill the drum in 8 hours and 9 hours respectively, while the third can empty it in 12 hours, how much time does it take for the drum to be filled. All three workers work simultaneously.
a) more than 7 hours
b) 8 hours
c) less than 3 hours
d) less than 1 hour
e) more than 5 hours
4. Three people C, D, E can do work in 20, 30, 40 days. The work, however, is to be done in 2 days. How many people who can complete the work in 120 days each have to be employed apart from C, D, E to do the work in correct time?
a) 17
b) 27
c) 37
d) 47
e) 57
5. If Kushal and Priya can do a piece of work in 5 days, Priya and Neha can complete a piece of work in 6 days and Kushal, Priya and Neha can complete the same work in 4 days, in how many days Kushal and Neha together will complete the same work?
a) 4.5 days
b) 7.5 days
c) 5.5 days
d) 6.2 days
e) 6.5 days
6. A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was
a) 9
b) 10
c) 11
d) 12
e) 13
7. A work is done by three person A, B and C. A alone takes 10 hours to complete a single product but B and C working together takes 4 hours, for the completion of the same product. If all of them worked together and completed 14 products, then how many hours have they worked?
a) 20 hours
b) 28 hours
c) 34 hours
d) 40 hours
e) 54 hours
8. Anil does a work in 90 days, Bittu in 40 days and Chintu in 12 days. They work one after another for a day each, starting with Anil followed by Bittu and then by Chintu. If the total wages received are Rs 360 and Anil, Bittu, Chintu share them in the ratio of the work done, find their respective individual wages.
a) Rs.40, Rs.60 and Rs.260
b) Rs.36, Rs.81 and Rs.243
c) Rs.42, Rs.86 and Rs.232
d) Rs.38, Rs.88 and Rs.234
e) none of these
9. If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?
a) 20 days
b) 40 days
c) 36 days
d) 30 days
e) 42 days
10. There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
a) 5
b) 6
c) 7
d) 8
e) 9
Solutions:
1. D) Let the rate of the outlet pipe be x m3/min.
Filling rate when both pipes are open
= (200 - x) m3/min ? (i)
Time taken for the tank to fill when both pipes are open = 20 minutes
Capacity of tank = 1400 m3
Therefore filling rate = 1400/20 = 70 m3/min …. (ii)
From (i) and (ii), we get,
200 - x = 70
x = 130 m3/min
If the inlet pipe is not open, the outlet pipe empties a
Completely filled tank in 1400/130 = 10 10/13 min
2. D) The number of days taken by the man, woman and child (working together) to complete the work = 6
Work done in 1 day when all 3 work together = 1/6
Let the man take m days to finish the task.
Number of days taken by a woman = 3m and number of days taken by a child = 6m
Work done by them in one day can be given as,
1/m + 1/3m + 1/6m = 1/6 => 9/6m = 1/6 => 6m = 54
Therefore, Time taken by the child alone to complete the job is 54 days.
3. E) Let A and B fill the drum while C empties it.
Let the capacity of the drum be 72 units.
Hence, A can fill 9 units, B can fill 8 units and C can empty 6 units.
- Total units filled per hour = 9 + 8 - 6 = 11
- Time taken = 72/11 = 6.54 hours
4. D) 1/20 + 1/30 + 1/40 + x/120 = ½
Where x is the number of men required
x/120 = 1/2 – 13/120 => x/120 = (60 – 13)/120 => x = 47
Therefore, 47 men are required to complete the work.
5. B) (Kushal + Priya)’s 1 day work = 1/5
(Priya + Neha)’s 1 day work = 1/6
(Kushal + Priya + Niha)’s 1 day work = ¼
Kushal's 1 day work = (Kushal + Priya + Neha)?s 1 days work - (Priya + Neha)?s 1 day work
Kushal's 1 day work = 1/4 – 1/6 = 1/12 … (i)
Neha's 1 day work = (Kushal + Priya + Neha)?s 1 days work - (Kushal + Priya)?s 1 day work
Neha's 1 day work = 1/4 – 1/5 = 1/20
Therefore (Kushal + Neha)’s 1 day work = 1/20 + 1/12 = 2/15
Therefore, time taken by Kushal and Neha to complete the work together is 15/2 i.e 7 ½ days.
6. a) (A + B)’s 1 day work = 1/45 + 1/40 = 17/360
Work done by B in 23 days = 1 × 23/40 = 23/40
Remaining work = 1 – 23/40 = 17/40
Now, 17/360 work was done by (A + B) in 1 day
17/40 work was done by (A + B) in 1 × 360/17 × 17/40 = 9
Therefore, A left after 9 days
7. D) According to the question,
1/A =10; 1/B + 1/C = 1/4; 1/B + 1/C + 1/A = 7/20
In 20 hours, working together, they will complete 7 products.
Thus, in 40 hours they will complete 14 products.
8. B) Assume there are 360 units of work (LCM of 90, 40 and 12).
Hence, A, B and C can do 4,9 and 30 units per day or together 43 units every 3 days.
So In 24 days, 43 × 8 = 344 units of work is completed. In the next 2 days, 13 units are completed and on 27th day, C takes (1/10)th of a day to finish the rest.
So, A and B worked for 9 days each and have hence put in 36 and 81 units respectively, and the rest of the 243 units is put in by C.
The wages shall also be distributed in the same ratio as: Rs 36, Rs 81 and Rs 243.
9. D) Let x be the number of days in which A can do the job alone
Therefore, working alone, a will complete (1/x)th of the job a day
Similarly, Let y be the number of days in which A can do the job alone
Therefore, working alone, a will complete (1/y)th of the job a day
Working together A and B will complete (1/x + 1/y)th of the job a day
The problem states that working together, A and B will complete the job in 7.5 day i.e, they will complete (2/15)th of the job a day.
=> 1/x + 1/y = 2/15 …. (i)
From the question, we know that if A completes half the job working alone and B takes over and completes the next half, they will take 20 days.
As A can complete the job working alone in 'a' days, he will complete half the job, working alone, in x/2 days
Similarly, B will complete the remaining half of the job in y/2 days
=> x/2 + y/2 = 20 => x + y = 40 … (ii)
From equations (i) and (ii) we have
1/(40 – y) + 1/y = 2/15 => 600 = 2y(40 – y) => y2 – 40y + 300 = 0
=> (y – 30) (y – 10) = 0
If y = 30 then x = 1 or if b = 10 then a = 30
As A is more efficient than B, he will take lesser time to do the job alone. Hence A will take only 10 days and B will take 30 days.
10. C) Let there be x fill pipes attached to the tank
Therefore, there will be 12 – x drain pipes attached to the tank
Each fill pipe fills the tank in 8 hours
Therefore, each of the fill pipes will fill (1/8)th of the tank in 1 hour.
Hence, x fill pipes will fill x/8 of the tank in an hour
Each drain pipe will drain the tank in 6 hours
Hence (12 – x) drain pipes will drain (12 – x)/6 of the tank in an hour
When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow.
Therefore, in an hour (1/24)th of the tank gets filled
Hence,
x/8 – (12 –x)/6 = 1/24 => 3x – 4(12 – x)]/24 = 1/24 => 7x – 48 = 1 => x = 7
Therefore there are 7 filling pipes