**Aptitude Problems - Time and Work**

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For solved problems on Time and work solved problems 1

**Quantitative Aptitude – Time and Work Solved Problem 21**

P can complete a piece of work in 18 days and B can do the same
piece of work in 15 days. They started working together but after 3 days P left
and Q alone completed the remaining work. The whole work was completed in
(approximately)

a) 12.5 days b) 8
days c) 14 days d) 14.5 days. e)18 days

**Answer: A**

**Explanation :**Both together worked for 3 days.

In 3 days , P can do = 3 x

1
18

=
1
6

th work
In
3 days, Q can do = 3 x

1
15

=
1
5

th
work
In 3 days , work finished =

1
6

+
1
5

=
11
30

Balance work =

19
30

Balance work finished by Q => Time taken
by Q to finish the balance work =

19
30

x 15 = 9.5 days
The
whole work was completed in 9.5 + 3 = 12.5 days.

**Quantitative Aptitude – Time and Work Solved Problem 22**

A can do a work in 36 days, B in 18 days and C in 24 days. B and
C start the work but are forced to leave after 6 days. The remaining work was
done by A in

a) 8 days b) 9
days c) 10 days d) 12 days e)15 days

**Answer : E**

**Explanation :**

In 6 days , B and C together finished => 6 x (

1
18

+
1
24

)
= 6 x

7
72

=
7
12

Balance work = 1-

7
12

=
5
12

A can do complete work in 36 days.

The remaining 5/12 th work done by A in =

5
12

X 36 = 15
days**Quantitative Aptitude – Time and Work Solved Problem 23**

A
can do a piece of work in 90 days and Y can do it in 80 days. They began working
together but A leaves after some days
and then B completed the remaining work in 46 days. The number of days after
which A left the work was

a)
15 days b) 7
days c) 10days d) 11 days e)16 days

**Answer: E**

**Explanation:**A and B did the work for some days.

After
that , B completed the remaining work in 46 days .

In
46 days, word done by B =

1
80

x 46
=
23
45

.
Remaining work = 1 –

23
45

=
17
45

Remaining
work is done by both A and B together =

17
45

x
90 x 80
90 + 80

= 16 days

**Quantitative Aptitude – Time and Work Solved Problem 24**

A is thrice as good a workman as B and therefore is able to
finish a job in 45 days less than B. Working together, they can finish the job in

a) 15 days b)
11.25 days c) 30 days d)
45 days e)60 days

**Answer : B**

**Explanation :**A is thrice as good a workman as B =>A = 3B

The ratio of efficiencies of A and B = 3:1

The
ratio of the days taken by A and B to finish work is = 1: 3

B takes 45 days to finish the
work => 3 parts = 45 days

A alone takes =>

45
3

x 1 =
15 days
A and B alone can finish the work is =

AB
A+B

=
15 X 45
15 + 45

=
11.25

**Quantitative Aptitude – Time and Work Solved Problem 25**

A woman can do a piece of work in 40 days. Man is 25% more
efficient than Woman. The number of days taken by man to do the same piece of
work is

a)12 days b) 16 days c) 25
days d) 32 days e)40 days

**Answer :D**

**Explanation :**The ratio of the efficiencies of a woman and man = 100 : 125

=
4 : 5

The ratio of the days
taken by woman and man to finish the work = 5 :4

Woman takes 32 days to finish
the work.=> 5 parts = 40

The number of days taken by man to
finish the work = 4 parts =

40
5

x 4 = 32 days**Quantitative Aptitude – Time and Work Solved Problem 26**

P is twice as good a workman as Q and Q is twice as good a
workman as R. If A and B can together finish a piece of work in 6 days, then C
can do it by himself in

a)10 days b)8
days c)
24 days d)36 days e)20 days

**Answer: D**

**Explanation:**Let P takes x days to finish the work, then Q takes 2x days and R takes 4x days.

Given
A and B together finish the work in 6 days => In 1 day A+B can do

1
6

of the
work
In 1 day A and B together can do
=>

1
x

+
1
2x

=
1
6

$\frac{3}{2x}$
= $\frac{1}{6}$

=>
2x=18 x=9

Therefore
R can do the work in 4x = 4 x 9 = 36 days

**Quantitative Aptitude – Time and Work Solved Problem 27**

A takes twice as much time as
B and C takes thrice as much time as B to finish a piece of work. Working
together they can finish the work in 18 days. The number of days need for B to
do the work alone is

a) 20 days b) 22 days c)
33 days d)44 days e)50 days

**Answer:C**

**Explanation:**Let A takes x days to complete the work , then B takes

x
2

days and C takes
3x
2

days to complete the work.
A,B and C together complete the work in
18 days

In
1 day , all they together can do =>

1
x

+
2
x

+
2
3x

=
1
18

ð $\frac{3+6+2}{3x}$
=

1
18

ð $\frac{3x}{2}$
= 18

ð X
= 66 days

The
number of days B alone takes to finish the work =

x
2

= 33 days**Quantitative Aptitude – Time and Work Solved Problem 28**

A can do a work in 20 days, B can do it in 30 days, while C can
do it in 12 days. In how many days will the work be completed if A and B are assisted by C on every third day?

a) 9 days
b) 15 days c) 18 days d) 27 days e)30 days

Answer:

Explanation
: On every third day , A+B are assisted by C

In
1 day A and B together can do =

1
20

+
1
30

=
5
60

=
1
12

In 3 days A and B together
can do = 3 x

1
12

=
1
4

work
On 3

^{rd}day ,C assists A and B => In 3 days total work done =
1
4

+
1
12

=
4
12

=
1
3

In 3 days,

1
3

rd work will
be completed
So
Total work is completed in 3 x 3 = 9
days

**Quantitative Aptitude – Time and Work Solved Problem 29**

A and B can separately do a piece of work in 20 and 15 days,
respectively. They worked together for 6 days, after which B was replaced by C.
The work was finished in next 5 days. The number of days in which C alone could
do the work is

a) 30 days b)
45 days c) 40 days d)
35 days e)50 days

Answer:
E

Explanation
: B worked for 6 days => In 6 days B completed = 6 x

1
15

=
2
5

th work
A worked for
first 6 days and later 4 days => In 10 days A completed = 10 x

1
20

=
1
2

of the work
Total
work done by A and B =

2
5

+
1
2

=
4+5
10

=
9
10

Balance work = 1-

9
10

=
1
10

th of total work
Balance work was completed by C in 5 days

C can do 1/10 of the work in 5 days.
Therefore C alone can do the work in 50 days.

**Quantitative Aptitude – Time and Work Solved Problem 30**

A and B together can complete a work in 15 days. A alone can
complete in 20 days. If B does the work only 1/3

^{rd}of a day daily, then in how many days A and B together will complete the work?
a) 10 days b) 20 days c) 11 days d)
15 days e)20 days

Answer:
In 1 day, A+B can do =

1
15

th work and
A alone can do =
1
20

^{th}of the work
B alone can do the work in 1 day , (A + B) – A =

1
15

–
1
20

4-3
60

=
1
60

th of the work
B alone can do the work in 60 days.

If
B works only

1
3

rd day => B alone can do the work in 3 x 60 = 180 days
Now
In 1 day , A+B can do =

1
15

+
1
180

=

(12+1)
180

=
13
180

A and B together will complete the work in

180
13

= 13
11
13

days if B does the work
1
3

rd day.**Quantitative Aptitude – Time and Work Solved Problem 31**

A can do a work in 24 days, B in 12 days and C in 6 days. B and
C start the work but are forced to leave after 3 days. The remaining work was
done by A in how many days?

a) 8 days b) 6 days c)
10 days d) 12 days e)15 days

**Answer:B**

**Explanation :**In 1 day A can do

1
24

th of the work , B can do
1
12

th of the work and C can do
1
6

of the work
In 3 days B completed = 1/12
x 3 = ¼ th work

In
3 days C completed = 1/6 x 3 = ½ of the
work

In 3 days B and C completed = ¼ + ½ = ¾ th
work

Balance
work = 1 – ¾ = ¼ th work

The
number of days A takes to complete the remaining work = ¼ x 24 = 6 days.

**Quantitative Aptitude – Time and Work Solved Problem 32**

A and B working separately can do a piece of work in 10 days and
15 days, respectively. If they work on alternate days beginning with A, in how
many days will the work be completed?

a) 18 days b) 13 days c) 12 days d) 6 days e)20 days

**Answer: C**

**Explanation :**A and B can do

1
10

and
1
15

th work in a day.
They
work on alternate days, beginning with A.

1

^{ST}day A works and on 2nd day B works.
In
2 days A+B can do =>

1
10

+
1
15

=

5
30

=
1
6

th of the work.
In
2 days ,

1
6

th of the work will be completed.
Total
work be completed in 6 x2 = 12 days

**Quantitative Aptitude – Time and Work Solved Problem 33**

A and B can do work in 18 and 24 days respectively. They
together undertook a piece of work for Rs 4200, what is the share of A?

a)
Rs 1800 b)Rs 2400 c)Rs 2500 d)Rs
3000 e)Rs 3600

**Answer : B**

**Explanation :**The ratio of the days taken by A and B = 18 : 24 = 3 :4

The ratio of the efficiencies of A and B =
4 :3

Wages
are always distributed based the efficiencies of the people involved in the
task.

Share of A in total Rs 4200 remuneration
= Rs 4200 x

4
7

= Rs 2400**Quantitative Aptitude – Time and Work Solved Problem 34**

A can do a work in 36 days and B can do the same work in 48
days. With the help of C , they finished the work in 12 days. What is the share
of C if their total remuneration is Rs 4800 ?

a)Rs 1800 b)Rs
600 c)Rs 1200 d)Rs 2000 e)Rs 2500

**Answer :C**

**Explanation :**Wages are distributed in proportion to the part of the work done by each individual.

A can do in 12 days =>

1
36

x 12 =
1
3

rd work
B can do in 12 days =>

1
48

x 12
=
1
4

rth work
A and B did = (

1
3

+
1
4

) =
7
12

th of the
work
Remaining
work done by C

Remaining work = 1-

7
12

=
5
12

Share of C in total remuneration Rs 4800 =
Rs 4800 x

5
12

=Rs 2000**Quantitative Aptitude – Time and Work Solved Problem 35**

A man and a boy received Rs 1600 as wages for 5 days for the
work they did together. The man’s efficiency in the work was four times that of
the boy. What are the daily wages of the boy?

a) Rs 76 b)Rs
56 c) Rs 64 d) Rs 40 e)Rs 50

**Answer : C**

**Explanation :**Man is 3 times efficient that of Boy => M = 4B

Ratio of the efficiency of M and
B M:B= 4 :1

Wages
are distributed in proportion to their efficiencies.

Total wages of Boy = Rs 1600 x

1
5

= Rs 320
Boy worked for 5 days , therefore daily
wages of Boy = Rs

320
5

= Rs 64**Quantitative Aptitude – Time and Work Solved Problem 36**

If 5 men or 7 women can earn Rs 10500 per day, how much would 7
men and 13 women earn per day?

a) Rs 34200 b)
Rs 31700 c) Rs 19500 d)Rs
17100 e)Rs 24000

**Answer: A**

**Explanation:**Daily earnings of 5 men = Rs 10500

Daily earnings of 1 man =

10500
5

= Rs 2100
Daily earnings of 7 women = Rs 10500

Daily earnings of 1 woman =

10500
7

= Rs 1500
Daily earnings of 7 men and 13 women = 7 x
2100 + 13 x 1500

= 14700 + 19500 = Rs 34200

**Quantitative Aptitude – Time and Work Solved Problem 37**

A , B and C completed a work costing Rs 3600. A worked for 6
days, B worked for 4 and C worked for 9 days. If the ratio of the daily wages
of A ,B and C are in the ratio 5 : 6 : 4, how much wages will be received by B
?

a)Rs 900 b)Rs
720 c)Rs 1080 d)Rs 960 e)Rs 1000

**Answer:D**

**Explanation:**Ratio of the wages of A , B and C respectively = 5 x 6 : 6 x 4 : 4 x 9

= 30 : 24 : 36 = 5 : 4 : 6

Therefore wages received by B = Rs 3600 x

4
5+4+6

= Rs 3600 x

4
15

= Rs 960

**Quantitative Aptitude – Time and Work Solved Problem 38**

1 man and 2 women together can complete a work in 14 days while 4 men and 2 women
together can do it in 8 days. If a woman gets Rs 1800 per day. How much should
a man get per day ?

a)Rs 1200 b)RS 1400 c) Rs 1440 d)Rs 1500 e)Rs500

**Answer : A**

**Explanation:**In 1 day 1M + 2W =

1
14

th work and 4 M +2 W
=
1
8

th work
14 M + 28 W = 1 and 32M + 16 W= 1

Equating both => 18 M = 12w => 3 M = 2 W

Therefore , 1 M =

2
3

W
Amount received by 1 man per day =
Rs 1800 x

2
3

= Rs 1200**Quantitative Aptitude – Time and Work Solved Problem 39**

A, B and C work for 7,8
and 10 days respectively and they together Rs 1440 for their work. If the ratio of their each
day’s work is

1
3

:
1
4

:
1
6

; then how much does A get ?
a)Rs 720 b)
Rs 600 c)Rs 560 d)Rs 800 e)Rs
400

**Answer: B**

**Explanation:**The ratio of each day’s work =

1
3

:
1
4

:
1
6

=

4
12

:
3
12

:
2
12

= 4 : 3 : 2

Ratio of the shares = 7 x4 :
8 x 3 : 10 x 2

= 28: 24 : 20 = 7 : 6 : 5

Share of A in the remuneration = Rs 1440 x

7
18

= Rs 560**Quantitative Aptitude – Time and Work Solved Problem 40**

A contractor
engaged 5 men to complete a work in 20 days. After 15 days , he engaged 3 more
men in order to complete the work on time. If additional men were not engaged ,
how many days beyond the schedule it
would have taken to complete the work ?

a)1 day b)2
days c)4 days d)5 days e)3 days

**Answer :E**

**Explanation**: Total man days= Men x Days

5 men worked for 15 days => Man
days = 5 x 15 = 75 days

Initial 5 men and additional 3 men
worked remaining (20 – 15) =5 days =>

Man days (5 +3) x 5 =40

Total man days = 75 +40 = 115

If
additional men not engaged , work done in = Number of man days / Number of Men

=

115
5

= 23
Days beyond the schedule = 23 – 20 =
3 days

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