Aptitude Problems  Time and Work
For Better Understanding of this chapter , Time and Work  Concept and Formulae
Quantitative
Aptitude – Time and Work Solved Problem 1
30 men can do a work in 25 days. In how
many days 20 men can do the same work ?
a)37.5 days b)40 days c)25
days d)45 days e)50 days
Answer: A
Explanation:
30 men can do the work in 25
days.
1 man can do the same work in 30 x 25 days
20 men will take =
(30 x 25)
20
= 37.5
days
Quantitative
Aptitude – Time and Work Solved Problem 2
A farmer can plough a filed working 10
hours day in 18 days. The farmer has to work how many hours per day to plough
the same field in 12 days?
a)12 hours b)12 hours c)18
hours d)15 hours e)None of these
Answer : D
Explanation :
Total hours to plough the field is 10 x 18 hours
Total hours to plough the field is 10 x 18 hours
To finish in 12 days =>
(10 X 18)
12
= 15 hours
Quantitative
Aptitude – Time and Work Solved Problem 3
64 men can do a piece of work in 30 days
working 12 hours day. In how many days 80 men complete the same piece of work
if they work for 16 hours a day ?
a)16 days b)
18 days c) 20 days d)24 days e)25 days
Answer :B
Explanation :
M1 D1 H1
W1
=
M2 D2 H2
W2
Here W1=W2 because they all performing same piece of work.
Here M1
= 64 D1= 30 and H1= 12 M2 =80
D2= ? H2= 16
M1D1H1 = M2D2H2
64 x 30 x 12 = 80 X D2 X 16
On
solving, we get D2 = 18 days
Quantitative
Aptitude – Time and Work Solved Problem 4
If 120 men can build a wall of 104 meters
long in 84 days for 8 hours a day , in how many days can 70 men build a similar
wall of 52 meters long working for 9 hours a day ?
a)
64 days b)40 days c)50 days d)56
days e) 60 days
Answer : A
Explanation : Here M1 = 120 D1= 84
H1= 8 W1= 104
M2 =70 D2= ?
H2= 9 W2= 52
M1 D1 H1
W1
=
M2 D2 H2
W2
120 x 84 x 8
104
=
70 x D2 x 9
52
On
solving, we get D2= 64 days
Quantitative
Aptitude – Time and Work Solved Problem 5
45 men can complete a work in 16 days. 7
days after they started working, 36 more men joined them. How many days will
they now take to complete the remaining work?
a) 5 days b)
8 days c) 9 days d)10.5 days e)12 days
Answer: A
Explanation:
Answer : M1=45 ,
M2= 45 +36 = 81 (36 more men joined)
D1= 16 7 = 9 days (4 days work is already done by 45 men)
D2
= ?
M1D1 =M2 D2
Ã° 45 x 9 = 81
X D2
Ã° D2
= $ \frac{45\times9}{81} $
>
Ã° D2
= 5 days
Aptitude
Questions – Time and Work Solved Problem 6
A road of 5 km length will be constructed
in 80 days. So, 420 workers were employed. But after 60 days, it was found that
only 3
1
2
km road was completed. Now, how many more people were needed to
finish the work in the specified time?
a) 480 b)80 c) 200 d)100 e)120
Answer:
Explanation: Total work is 5 km . Work completed = 3 ½ =
7
2
km
Remaining work =
3
2
km
To finish in time , they have only 20 days ( 80 60) to
complete the balance work .( Because already 420 workers worked for 60 days)
M1= 420 D1=60
W1=
3
5
km M2= ? D2= 20 W2=
3
2
M1 D1
W1
=
M2 D2
W2
Ã° $\frac{420\times60}{7/2}$ = $\frac{M2\times20}{3/2} $
Ã° 420
x 60 x $ \frac{3}{2}
$ = M2 X 20 X $\frac{7}{2} $
Ã° M2=
420 X 60 X 3
20 X 7
Ã° M2
= 540
Required
number of additional men = 540 – 420 = 120
Arithmetic
Aptitude Questions – Time and Work Solved Problem 7
The typing speed of A and B together is
350 words in 5 minutes whereas A can type 200 words in 4 minutes. How many
words can B type in 1 minute ?
a)10 word b)20
words c)30 words d)40 words e)50 words
Answer : B
Explanation :
Together can type 35 words in 5 minutes =>In 1 minutes , they together can
type
350
5
= 70 words per minute .
A along can type
200
4
= 50 words per minute.
Therefore , B
along can type 70 – 50 = 20 words per
minute
Aptitude
MCQ with Answers – Time and Work Solved Problem 8
Ramya takes 10 days to complete a piece
of work and Radha takes 15 days to do the same work. In how many days they
together will do the same work ?
a) 25 days b) 20 days c) 12 days d) 8 days e) 6 days
Answer : E
Explanation :
In 1 day , ramya can do
1
10
th of the work
In 1 day ,Radha can do
1
15
th of the work
In 1 day , Ramya and Radha can do (
1
10
+
1
15
) =
5
30
=
1
6
^{th} of the work
So they
both together can do the work in 6 days
Shortcut : If a A can do a work in A days and B can do in
B days, the both together can do the work in AB/ A+B days.
AB/ A+B =>
10 x 15
10 +15
= 6 days
Quantitative
Aptitude Questions and Answers – Time and Work Solved Problem 9
A can do a job in 20 days. B takes 30
days and C finishes it in 60 days. If they all work together, how long will
they take to complete the job ?
a) 9 days b)11.5 days c) 12
days d) 10 days e)20 days
Answer: D
Explanation: In 1 day, A can do
1
20
of the job, B can do
1
30
th of the job and C can do
1
60
^{th} of the job.
Therefore in 1 day , A+B+C can do =
1
20
+
1
30
+
1
60
=
(3+2+1)
60
=
1
10
th of the job
So A,B and C together can do the job 10 days
Aptitude
Problems and answers – Time and Work Solved Problem 10
A and B take 12 days to do a piece of
work, B and C take 15 days, C and A take 20 days. If A, B and C work together,
they will complete the work in
a) 9
days b) 18 days c) 12 days d) 16 days e)20 days
Answer :C
Explanation :
A+B can do
1
12
th of the work in a day , B+C can do
1
15
th of the work in a
day and C+A can do
1
20
th of the work
in a day.
In 1 day , (A+B)
+ (B+C) +(C+A) can do =
1
12
+
1
15
+
1
20
2A+2B+2C =
(5 + 4 + 3)
60
2(A+B+C)=
1
5
A+B+C =
1
10
Therefore , A,B and C together can do the job in 10
days
Arithmetic
Problems with Solutions – Time and Work Solved Problem 11
In the above problem , in how many days A
alone can do the work ?
a)
30 days b)60 days c)75 days d)50
days e)90 days
Answer :
Explanation : In 1 day A alone can do = (A+B+C)’s 1 day
work – (B+C)’s 1 day work
(A+B+C ) (B+C) =
1
10
–
1
15
A =
(32)
30
=
1
30
A alone can do the work in 30 days
Quantitative
Aptitude Test Questions – Time and Work Solved Problem 12
A can do a piece of work in 5 days, but
with the help of B, he can do it in 3 days. In what time can B do it alone ?
a) 8 days b) 6 days c)
7
1
2
days d) 15
days e)20 days
Answer :
Explanation : A with the help of B can do the work in 3
days .
In
1 day (A+B) can do
1
3
of the work
In 1 day A alone can do
1
5
of the work.
In 1 day , B
alone can do (A+B) A =
1
3
–
1
5
B
=
53
15
=
2
15
th of the work
B alone can do
15
2
= 7 ½ days
Aptitude
Questions and Answers – Time and Work Solved Problem 13
A can complete a piece of work in 16 days
and B can do the same job in 12 days. With the help of C, they did the job in 4
days only. Then, C alone can do the job in :
a) 4
4
5
days b) 8
3
5
days c) 9
3
5
days d) 24 days
e)30 days
Answer :
Explanation :
A and B with help of C, did the work in 4 days
In 1 day (A+B+C)
can do =
1
4
th work
In 1 day (A+B) can do = (
1
16
+
1
12
)th of the work
C alone can do
in 1 day => (A+B+C) –(A+B) =
1
4
(
1
16
+
1
12
)
Ã° C = 12 – $ \frac{3+4}{48}$
=> C =
5/48 th work
Therefore C alone can do the work in
48
5
= 9
3
5
days.
Quantitative
Aptitude Solved Questions– Time and Work
Solved Problem 14
Soumya alone can do ¼ of the work in 2.5 days and Sravani can do
1
3
of the
work in 4 days.In how many days Soumya and Sravani working together will finish
the work ?
a)
5 $ \frac{5}{11}$
days b)6 days c)9
days d)10 days e)15 days
Answer :A
Explanation :
Soumya can do ¼ of the work in 2.5 days => Soumya
can do the work in 4 x 2.5 = 10 days
Sravani can do
1
3
of the work in 4 days => Sravani
can do the work in 3 x 4 = 12 days
In 1 day ,
Soumya can do
1
10
th of the work
In 1 day ,
Sravani can do
1
12
th of the work
In 1 day , they
both together can do =>
1
10
+
1
12
=
11
60
They
both together can the work in
60
11
= 5 5/11 days
Arithmetic
Word Problems – Time and Work Solved
Problem 15
A and B can do a work in 15 days and 25 days
respectively. A worked for 9 days and left the work .In how many B can complete
the remaining work ?
a)
5 days b)8 days c)10 days d)15
days e)18 days
Answer: C
Explanation : In 1 day A can do
1
15
th of the work
In 9
days, A completed = 9 x
1
15
=
3
5
th of the work
Balance work = 1
–
3
5
=
2
5
th of the work
B can
complete the remaining
2
5
th work =
2
5
x 25 = 10 days
Arithmetic
Aptitude Solved Questions– Time and Work Solved Problem 16
A can do a job in 48 days. He worked for
12 days and then B completed the remaining work in 30 days. In how many days A
and B together can finish the work?
a)10 10/11 days b)20 days c)21 9/11 days d)25 days e)22 6/11 days
Answer :
Explanation : In 1 day , A can do
1
48
th work.
In 12
days , A completed 12 x
1
48
=
1
4
of
the work
B completed
remaining ¾ of the work in 30 days.
B can do the
complete work in 30 x
4
3
= 40 days
In 1 day ,
B can do
1
40
th work.
In 1 day A and
B together can do =
1
48
+
1
40
=
(5 + 6)
240
=
11
140
A and B
together can do the work in
240
11
= 21
9
11
days
Quantitative
Reasoning Solved Questions – Time and Work Solved Problem 17
20 men can do work in 30 days. 30 women
can do it in 32 days. In how many days 10 men and 8 women can do the same work
?
a)20days b)25
days c)28 days d)40 days e)15
days
Answer :
Explanation :
20 men can do the work in 30 days
=> In 1 day , 1 man can do
1
20 x 30
th of the work
30 women can do the work in 32 days
=> In 1 day, 1 woman can do
1
30 x 32
of the work.
In 1 day 10 men and 8 women can do => 10M + 8 W
= 10 X
= 10 X
1
20
X30 + 8 X
1
30
X 32
=
1
60
+
1
120
=
3
120
10 M + 8 W
can do the work in
120
3
= 40 days
Aptitude
Questions and Answers – Time and Work Solved Problem 18
16 men or 20 women can do a work in 30
days. In how many days 24 men and 10 women can do the same work ?
a)15 days b)18
days c)20 days d)25
days e)30 days
Answer : A
Explanation : 16 men can do the work in 30 days
=>In
1 day 1 man can do =
1
30 x 16
th work
20 women can do the work in 30 days
=> In 1 day, 1 woman can do =
1
20 x 30
th work
In 1 day 24 men and 10 women can do =
24 x
24 x
1
16 x 30
+ 10 x
1
20 x 30
=
1
20
+
1
60
=
4
60
=
1
15
24M +
10W can do the work in 15 days
Aptitude Questions with Solutions– Time and
Work Solved Problem 19
20men can do a job in 25days and 30 women
can do the same in 35 days. What is the ratio between the capacities of a man
and a woman ?
a)7:5 b)5:7 c)3:2 d)2
:3 e)7 :10
Answer : A
Explanation :
The number of days taken by 1 man to finish the work = 20 X 25 = 500
The number of the days taken by 1 woman to finish the
work = 30 x 35 = 700
Ratio
of the days taken by 1 man and 1 woman = 500 : 700 = 5 :7
Ratio between the capacities of a man and a woman
= Inverse ratio of the days taken by them = 7
:5
GMAT
Word Problems Aptitude – Time and Work
Solved Problem 20
A can do a work in 12 days. When he had
worked for 3 days, B joined him. If they complete the work in 3 more days, in
how many days can B alone finish the work?
a) 6 days b)
12 days c) 4 days d)
8 days e)10 days
Answer:
Explanation:
In 3 days , A finished = 3 x
1
12
= ¼ th of the work
Remaining work is completed by both A and B in 3 days
=> Balance ¾
work completed by A+B together in 3 days =
3
4
W = 3 days =>W= 4 days
(A+B) can do the complete work in 4 days.
In 1 day B can
do => (A+B) A =
1
4

1
12
=
3
1
12
=
1
6
B alone can finish the work in 6 days.
For more problems on Time and Work , visit Time and Work Solved Problems 2
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