Time
and Work Practice Problems Set – 1
1. An inlet pipe fills a tank of capacity 1400 m^{3} at
the rate of 200 m^{3}/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
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 m^{3}/min.
Filling rate when both
pipes are open
= (200 - x) m^{3}/min
? (i)
Time taken for the tank
to fill when both pipes are open = 20 minutes
Capacity of tank = 1400 m^{3}
Therefore filling rate =
1400/20 = 70 m^{3}/min …. (ii)
From (i) and (ii), we
get,
200 - x =
70
- x =
130 m^{3}/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) => y^{2} – 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