TIME AND
DISTANCE , TIME AND
WORK , Pipes and Cisterns
Time and Work Solved Problems on Basics:-
1. A can do a
work in 10 days. What is A’s 1 day work?
Ans: 1/10th of
work
2. Two people
can do a work in 10 days. What is 1 day 1 man work?
Ans: Since it is given
as 2 people can do a work in 10 days, total work is 10 * 2 = 20 units of work.
Therefore,
one day one man work = 1/total work = 1/20 units of work
3. Three men
can do a work in 15 days. One man can do a work in how many days?
Ans: Since it is given
as 3 people can do a work in 15 days, total work is 15 * 3 = 45 units of work.
Therefore,
one man can complete the work in 45 days
4. One man
one day work is 1/25. In how many days, can he finish the work?
Ans: Number of days required
= 1/(1/25) = 25 days
Difficulty Level – Medium :-
1. A can
work on 1km railway track in 1 day. In how many days, will he able to complte
the work on 12km railway track?
Soln: no. of days = total
work / work done in 1 day
Therefore, no. of days
taken = 12/1 = 12 days
2. A can
complete the work in 15 days. What fraction of work will be completed in 1 day?
Soln.: Let
the total work is 1 unit.
Work in 1day = total
work/no. of days to complete
=
1/15th of work
3. A can do
a piece of work in 3 days and B can do a piece of work in 5 days. In how many
days will the work be completed if both A and B work together?
Soln.: Using
formula:
Work done
by A in 1 day = 1/3
Work
done by B in 1 day = 1/5
Total
work done by A and B in 1 day = 1/3 + 1/5 = 8/15
Therefore,
no. of days to complete work by A and B together = 1/(Total work) = 1/(8/15) =
15/8 days which is less than 3 and 5
Using
shortcut/analysis/assumption
Let us
consider the total work be 15 units (LCM of 3 and 5)
So
work done by A in 1 day = 15/3 = 5 units
Similarly
work done by B in 1 day = 15/5 = 3 units
So
total work done by A and B in 1 day = 5 + 3 = 8 units
Therefore,
no. of days to complete total work i.e. 15 units = total work/work done in 1
day = 15/8 days
Note:
a. Work done by A and B in 1
day will always be greater than that of A and B individually
b. No. of days taken by A and B together will always be less
than that of A and B individually
Problems: -
Paper-I
1)A
pipe can fill a tank in 15 hrs. The tank develops a hole and 10% of water leaks out. The pipe will now fill the bank in
_____ .
a)
16 hrs 40 minutes b) 18 hrs 40 minutes
c)20
hrs d) 17 hrs 30 minutes Ans :a
2)A
125 metres long train overtakes a man walking at the rate of 4 kg/hr, parallel
to the line in the same direction, in 9 seconds. The speed of the train is
____ km/hr.
a)48 b 54 c) 80 d) 100 Ans:b
3)A
clerk walks from his house at 4 km/hr and reaches his office 5 minutes late. If
his speed is 5 km/hr , he will reach his office 10 minutes early. How far is
his from his home?
a)
5KM b) 5/12 KM c) 5/2 KM d) 15 KM
Ans : a
4)
A group of 10 students working an hour per day complete a work in 12 days. 12
students in the group working one hour per day will be able to finish it in
____ days
a)
8 b) 9 c) 10
d) 11 Ans:c
5)
Two taps A and B fill a tank separately in 24 minjutes and 40 minutes
respectively and a waste pipe C releases 30 litres per minutes. If all
the pipes are opened the tank is filled in a hour. The capacity of the tank is
______ litres
a)
750 b) 900 c) 800
d) 600 Ans : d
6)
Ravi rows a distance of 1 km down the
stream in 10 minutes and takes 30 minutes to cover the same distance up stream.
The speed of the stream is _______ km per hour.
a)
5 b) 3
c ) 2 d) 4 Ans : c
7)
Meena can type 500 words in 10 minutes and Leena can type 400 words in 10
minutes. They can together type 3600 words in _____ minutes.
a)
50 b) 40 c) 80
d) 100 Ans: b
8)
It takes an hour for a saree to dry in
the sun. 25 such sarees will dry in _____
a)
50 hrs b) 20 hrs c) 1 hr
d) 625 hours Ans : c
9)
A moneky ascends a greased pole 21 m high. In the first minute he ascends 5 m
and in the next minutes he descends 3 m.
If he continues this process, in how many minutes will he reach the top?
a)
17 minutes b) 10.5 minutes c) 21 minutes d) 40 minutes Ans: a
10)
Two pipes A and B fill a cistern in 24 minutes and 32 minutes respectively.
Assuming that both pipes are opened simultaneously, when must the first tap be
turned off so that the cistern may be filled in 16 minutes?
a)
after 10 minutes b) after 12
minutes c) after 8 minutes d) after 16 minutes Ans:b
11)
A train running at a speed of 54 km/hr passes a signal post in 18 seconds. The
length of train is
a)
432 m b) 150 m c) 120m
d) Data inadequate Ans : c
12)
A car is 25 km ahead of a scooter. The car travelling at 40 km / hr and the
scooter at 50 km / hr. The scooter will
overtake the car after _____
a)
1 ½ hr b) 2 ½ hr c) 3 ½ hr
d) 3 hrs. Ans : b
13)
Hari singh can cover a circular path of radius 21 m in 44 sec. He will cover a
distance of 3 km in _____
a) 16 minutes 20
seconds b) 16 minutes 40 seconds Ans : b
c)18 minutes 00 seconds d) 18 minutes 30 seconds
14)
Two cars start from one point and move along two roads at right angles to each other. Their speeds are 36
km/hr and 48 km /hr respectively. After
15 seconds the distance between them will be
a)
400 m b) 150 m c) 300 m
d) 250 m An s : d
15)
Ram, Mohan and Hari can do a work in 15 dayhs, 6 days and 10 days respectively.
All the three can together finish three times of that work in ____ days
a)
21 b) 18 c) 9
d) 15 Ans : c
16)
A,B, and C are employed to do a piece of job for Rs.529. A and B together are supposed to do 19/23 of
the work . C should be paid ____
a)
Rs.115 b) Rs.92 c) Rs.200
d) Rs.250 Ans : b
17)A
and B undertook to do a piece of work for Rs.4500. A alone could do it in 3 days and B in 12
days. with the help of C, they finish the work in 4 days. The share of C in the
money is ____
a)Rs.2250 b) 1500
c) 750 d) Rs.375 Ans: c
18)
A tank has a capacity of 240 litres. A pipe can empty 1/4th of the
tank in 5 minutes and another pipe can empty 1/3rd of the tank in 6
minutes. The tank is filled and both the pipes are opened for 3 minutes . How
much of the water is now left in the tank?
a)
160 litres b) 164 litres c) 196 litres d) 200 litres Ans: b
19)
Hira, Radhu and Kalu working alone can do a piece of work in 9,8 and 6 days
respectively. They jointly finish the work and earn Rs.522. The earnings should
be divided in the ratio of
a)
6:9:8 b) 9:8:6 c) 8:9:12
d) 6:8:9 Ans : c
20)
Javed walks at the rate of 3Km/hr for 2
hours and then at the rte of 2 km/hr for 3 hours. His average speed is ____
Km/hr
a)
4 b) 2.4 c) 2.5
d) 5 Ans: b
21)
Rohit can row 18 km in 4 hrs down stream but while returning h takes 12 hours.
The speed of the water current is
a)
1.5 km/hr b) 4 km / hr c) 2 km / hr d) 3 km/hr Ans: a
22)
Two persons move towards each other form two places 55 km apart. One moves at a speed of 12 km/hr and
other at 10 km/hr. They will be first 11 km apart from moving for
a)
3 hrs b) 2 hrs c) 6 hrs
d) 4hrs Ans : b
23)
Sixteen men complete a work in fifteen days.
Twenty four children can do the same work in twenty days. In how many
days will eight men and eight children together complete the same job?
a)
16 b) 15
c) 20 d) None of these Ans: c
24)
Kishan cycles at a speed of 8 km/hr . After every 10 km, he rests for 20
minutes. How long will he take to travel a distance of 40 Km?
a)
6 hrs 20 min b) 8 hrs c) 6 hrs d) 5 hrs
Ans:c
25)
Three pipes are connected to a tank. Pipes A and B connected with tubewells can
fill the tank in 10 hrs and 12 hrs respectively, while pipe C meant for
watering the garden can empty the tank in 6 hrs. At 7 a.m. all the three pies are opened. One fourth of the tank will
be filled at ____
a)
9 p.m. b) 10 p.m . c) 8 p.m.
d) 11 p.m. Ans: b
26)
Shivani can do a piece of work in 16 days, Babu in 24 days and with the help of
Sita, they finish it in 8 days. Sita can alone do it in
a)
40 days b) 60 days c) 48 days
d) 24 days Ans:c
27)
A and B can do a piece of work in 24 days, B and C can do it in 18 days and A
and C in 12 days. Working together they will finish the work in nearly
a)
9 days b) 10 dys c) 11 days and d) 8 days Ans:c
28)
Ram can complete a work in 12 days, while Rajan can finish it in 18 days. Ram works on it for 8 days and then Rajan
starts working on it. The work will be finished in
a)
6 days b) 7 days c) 8 days
d) 9 days Ans : a
PAPER - II
1.
A can do a piece of work in 30 days while B alone can do it in 40 days. In how
many
days can A and B working together do it ?(a) 17 1/7 (b) 27 1/7 (c) 42 3/4 (d)
70
2.
A and B together can complete a piece of work in 35 days while A alone can
complete
the same work in 60 days. B alone will be able to complete
the
same work in :
(a)
42 days (b) 72 days (c) 84 days (d) 96 days
3.
A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of
7
hours
each. How long will they take to do it, working together 8 2/5 hours a day ?
(a)
3 days' (b) 4 days (c) 4 1/2 days (d) None of these
4.
A can do a piece of work in 15 days and B alone can do it in 10 days. B works
at it
for
5 days and then leaves. A alone can finish the remaining work in :
(a)
13/2 (b) 15/2 days (c) 8 days (d) 9 days
5.
A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 days. In
how
many
days both A and B together can do the work?
(a)
7 ¾ (b)8 4/5 (c) 9 3/8 (d) 10
6.
A can do a piece of work in 80 days. He works at it for 10 days and then B
alone
finishes
the remaining work in 42 days. The two together could complete the work
in
:
(a)
24 days (b) 25 days (c) 30 days (d) 35 days
7.A
and B can together finish a work in 30 days. They worked at it for 20 days and
then
B left. The remaining work was done by A alone in 20 more days. A alone can
finish
the work in :
(a)
48 days (b) 50 days (c) 54 days (d) 60 days
8.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)
6 (b) 8 (c) 9 (d) 12
9.
A does half as much work as B in three-fourth of the time. If together they
take 18
days
to complete the work, how much time shall B take to do it ?
(a)
30 days (b) 35 days (c) 40 days (d) none of these
10.
A can do a certain job in 12 days. B is 60% more efficient than A. The number
of
days,
it takes B to do the same piece of work, is :
(a)
6 (b) 6 ¼ (c) 7 ½ (d) 8
11.
A can do a certain job in 25 days which B alone can do in 20 days. A started
thework and was joined by B after 10 days. The number of days taken in completing
the
work was :
(a)
12 ½ (b) 14 2/9 (c) 15 (d) 16 2/3
12.
A is twice as good a workman as B and together they finish a piece of work in
14
days.
The number of days taken by A alone to finish the work, is :
(a)
11 (b) 21 (c) 28 (d) 42
13.
A is thrice as good a workman as B and takes 10 days less to do a piece of work
than
B takes. B alone can do the whole work in :
(a)
12 days (b) 15 days (c) 20 days (d) 30 days
14.
A can do a piece of work in 14 days which B can do in 21 days. They begin
together
but 3 days before the completion of the work, A leaves off. The total
number
of days to complete the work is :
(a)
6 3/5 (b) 8 ½ (c) 10 1/5 (d) 13 ½
15.
If Ramesh, Suresh and Harish can do a piece of work in 15 days, 10 days and 6
days
respectively, how long will they take to do it, if all the three work at it
together?
(a)
3 days (b) 3 ½ days (c) 3 9/20 days (d) 3 3/20 days
16.
A and B can do a piece of work in 72 days; B and C can do it in 120 days; A and
C
can do it in 90 days. In what time can A alone do it ? (a) 150 days (b) 120
days (c) 100 days (d) 80 days
17.
A and B can do a piece of work in 5 days; Band C can do it in, 7 days; A and C
can
do it in 4 days. Who among these will take the least time if put to do it
alone?
(a)
A (b) B (c) C (d) Data inadequate
18.
If A, B and C together can finish a piece of work in 4 days; A alone can do it
in
12
days and B in 18 days, then C alone can do it in :
(a)
21 days (b) 16 days (c) 14 days {d) 9 days
19.
A and B can do a piece of work in 18 days; Band C can do it in 24 days; A and C
can
do it in 36 days. In how many days can they do it all working together'?
(a)
12
(b) 13 (c) 16 (d) 26
20.
A and B together can do a piece of work in 12 days, which Band 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) 24 (c) 36 (d) 48
21.
A is twice as good a workman as B and together they complete a work in 15
days.
In how many days can the work be completed by B alone?)
(a)
22 ½ (b) 30 (c) 37 ½ (d) 45
22.
45 men can complete a work in 16 days. Six days after they started working, 30
more
men joined them. How many days will they now take to complete the
remaining
work?
(a)
4 (b) 5 (c) 6 (d) 8
23.
12 men can complete a work in 18 days. Six days after they started working, 4
men
joined them. How many days will all of them take to finish the remaining
work?
(a)
9 (b) 10 (c) 12 (d) 15
24.
Twelve men can complete a work in 8 days. Three days after they started the
work,
3 more men joined. In how many days will all of them together complete the
remaining
work?
(a)
2 (b) 4 (c) 5 (d) 6
25.
A, B and C are employed to do a piece of work for Rs. 529. A and C are
supposed
to finish 19/23 of the work together. How much shall be paid to B ?
(a)
Rs. 82 (b) Rs. 92 (c) Rs. 300 (d) Rs. 437
26.
A job is completed by 10 men in 20 days and by 20 women in 15 days. How many
days
will it take for 5 men and 10 women to finish that work?
(a)
17 ½ (b) 17 1/7 (c) 17 (d) 17 1/120
27.
A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4
women
in 10 days. It can be done by 9 men and 15 women in :
(a)
1 day (b) 2 days (c) 3 days (d) 4 days
28.
4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in
10
days. In how many days will 10 women working together finish it ?
(a)
24
(b) 32 (c) 36 (d) 40
29.
12 children take 16 days to complete a work which can be completed by 8 adults
in
12 days. 16 adults started working and after 3 days 10 adults left and 4
children
joined
them. How many days will it take them to complete the remaining work?
(a)
6 (b) 8 (c) 4 (d) 3
30.
Ram can do a piece of work in 8 days which Shyam can finish in 12 days. If they
work
at it on alternate days with Ram beginning, in how many days, the work will
be
finished?
(a)
9 1/3 (b) 9 ½ (c) 91/24 (d) 10 1/3
31.
A and B working separately can do a piece of work in 9 and 12 days
respectively.
If
they work for a day alternately, A beginning, in how many days the work will be
completed?
(a)
10 ½ (b) 10 1/3 (c) 10 ¼ (d) 10 2/3
32.
A, Band C can do a piece 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 Band C on
alternate
days?
(a)
7 days (b) 8 days (c) 9 days (d) 10 days
33.
Machines A and B produce 8000 clips in 4 and 6 hours respectively. If they work
alternately
for 1 hour, A starting first, then 8000 clips will be produced in :
(a)
4 1/3 hours (b) 4 2/3 (c) 5 1/3 hrs (d) 5 2/3 hrs
34.
A father can do a job as fast as his two sons working together. If one son does
the
job
in 3 hours and the other in 6 hours, how many hours does it take the father to
do
the
job?
(a)
1 (b) 2 (c) 3 (d) 4
35.
A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28
days.
The same money is sufficient to pay the wages of both for:
(a)
12 days (b) 14 days (c) 12 ¼ days (d) 24 ½ days
36.
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can
do
the same work in 8 days. In how many days can 2 men and 1. boy do the work?
(a)
12 ½ days (b)14 (c)17 (d)8
37.
A is twice as good a workman as B and together they finish a
piece
of work in 18 days. In how many days will A alone finish the work?
a. 37 b. 27 days c. 67
d. 44
38.
A and B undertake to do a piece of work for Rs. 600. A alone
can-
do it in 6 days while B alone can do it in 8 days. With the help of C, they
finish
it
in 3 days. Find the share of A?
a.
Rs. 400
b.
Rs. 800
c.
Rs. 300
d.
none
39.
A and B undertake to do a piece of work for Rs. 600. A alone
can
do it in 6 days while B alone can do it in 8 days. With the help of C, they
finish
it
in 3 days. Find the share of B?
a.Rs.
400
b.Rs.
800
c.Rs.
300
d.Rs.225
40.
A and B undertake to do a piece of work for Rs. 600. A alone
can-
do it in 6 days while B alone can do it in 8 days. With the help of C, they
finish
it
in 3 days. Find the share of c?
(a)
Rs. 75 b. 27 days c. 67 d. 44
41.
A and B can do a piece of work in 12 days; Band C can do it
in
15 days ; A and C can do it in 20 days. In how many days will A, Band' C finish
it,
working
all together?
(a)
10 days b. 27 days c. 67 d. 44
42.
A and B can do a piece of work in 12 days; Band C can do it
in
15 days ; A and C can do it in 20 days. find the number of days taken by A to
finish
it working alone.
(a)
30 days b. 27 days c. 67 d. none
43.
A and B can do a piece of work in 12 days; Band C can do it
in
15 days ; A and C can do it in 20 days. find the number of days taken by B to
finish
it working alone.
(a)
30 days b. 20 days c. 67 d. none
44.
A and B can do a piece of work in 12 days; Band C can do it
in
15 days ; A and C can do it in 20 days. find the number of days taken by C to
finish
it working alone.
(a)
60 days (B) 30 days C. 20 days D. NONE
45.
A is twice as good a workman as B and together they finish a
piece
of work in 18 days. In how many days will A alone finish the work?
(a)
27 days (B) 30 days C. 20 days D. NONE
46.
A and B undertake to do a piece of work for Rs. 600. A alone
can-
do it in 6 days while B alone can do it in 8 days. With the help of C, they
finish
it
in 3 days. Find the share of A?
(a)
Rs. 300 (B) 30 days C. 20 days D. NONE
47.
A and B undertake to do a piece of work for Rs. 600. A alone
can-
do it in 6 days while B alone can do it in 8 days. With the help of C, they
finish
it
in 3 days. Find the share of B?
(a)
Rs.225 (B) 30 days C. 20 days D. NONE
48.
A can do a piece of work in 10 days which B alone can do in 12
days.
In how many days will they finish the work, both working together?
(a)
5 5/11 days b. 27 days c. 67 d. 44
49.
Two persons A and B working together can dig a trench in 8 hours while A alone
can
dig it in 12 hours. In how many hours B alone can dig such a trench?
(a)
25 hours (b) 24 hours (c) 42 hours (d) none
50.
Ex. 4. 3 men can complete a piece of work in 6 days. Two days after
they
started the work, 3 more men joined them. How many days will they take to
complete
the remaining work?
(a)
25
hours (b) 24 hours (C) 2 days d) n0ne
(a)
ANSWERS:
FOR
PAPER – II:-
1.
(a) 2.(c) 3.(a) 4.(b) 5.(c)
6.(c)
7.(d) 8.(c) 9.(a)10. (c)
11.(d)
12.(b) 13.(b) 14.(c) 15.(a)
16.(b)
17.(a) 18.(d) 19(c)20. (b)
21.(d)
22(c) 23.(a) 24.(b) 25.(b)
26.(b)
27.(c) 28(d) 29(a)30.(b)
31.(c)
32.(b) 33.(b) 34.(b) 35.(a)
36.A
37.B 38.C 39.D 40.A
41.A
42.A 43.B 44.A 45. A
46.A
47.A 48.A 49.B 50.C
No comments:
Post a Comment