 A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :


Answer: Option DExplanation:
A’s 1 day’s work =

1

;

15

B’s 1 day’s work =

1

;

20

(A + B)’s 1 day’s work =


1

+

1


=

7

.

15

20

60

(A + B)’s 4 day’s work =


7

x 4


=

7

.

60

15

Therefore, Remaining work =


1 –

7


=

8

.

15

15

 A can laid railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:


Answer: Option CExplanation:
(A + B + C)’s 1 day’s work =

1

,

4

A’s 1 day’s work =

1

,

16

B’s 1 day’s work =

1

.

12

C’s 1 day’s work =

1

–


1

+

1


=


1

–

7


=

5

.

4

16

12

4

48

48

So, C alone can do the work in

48

= 9

3

days.

5

5

 A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

A. 
12 days 
B. 
15 days 
C. 
16 days 
D. 
18 ays 

 A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A. 
Rs. 375 
B. 
Rs. 400 
C. 
Rs. 600 
D. 
Rs. 800 
Answer: Option B
Explanation:
C’s 1 day’s work =

1

–


1

+

1


=

1

–

7

=

1

.

3

6

8

3

24

24

A’s wages : B’s wages : C’s wages =

1

:

1

:

1

= 4 : 3 : 1.

6

8

24

C’s share (for 3 days) = Rs.


3 x

1

x 3200


= Rs. 400.

24


 A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A. 
20 days 
B. 

C. 
25 days 
D. 
30 days 

 If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

A. 
4 days 
B. 
5 days 
C. 
6 days 
D. 
7 days 
Answer: Option A
Explanation:
Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.
Then, 6x + 8y =

1

and 26x + 48y =

1

.

10

2

Solving these two equations, we get : x =

1

and y =

1

.

100

200

(15 men + 20 boy)’s 1 day’s work =


15

+

20


=

1

.

100

200

4

15 men and 20 boys can do the work in 4 days. 
 A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

A. 
23 days 
B. 
37 days 
C. 
37 
D. 
40 days 
Answer: Option C
Explanation:
Whole work is done by A in


20 x

5


= 25 days.

4

Now,


1 –

4


i.e.,

1

work is done by A and B in 3 days.

5

5

Whole work will be done by A and B in (3 x 5) = 15 days.
A’s 1 day’s work =

1

, (A + B)’s 1 day’s work =

1

.

25

15

B’s 1 day’s work =


1

–

1


=

4

=

2

.

15

25

150

75

So, B alone would do the work in

75

= 37

1

days.

2

2


 A machine P can print one lakh books in 8 hours; machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?

A. 
11:30 A.M. 
B. 
12 noon 
C. 
12:30 P.M. 
D. 
1:00 P.M. 
Answer: Option D
Explanation:
(P + Q + R)’s 1 hour’s work =


1

+

1

+

1


=

37

.

8

10

12

120

Work done by P, Q and R in 2 hours =


37

x 2


=

37

.

120

60

Remaining work =


1 –

37


=

23

.

60

60

(Q + R)’s 1 hour’s work =


1

+

1


=

11

.

10

12

60

Now,

11

work is done by Q and R in 1 hour.

60

So,

23

work will be done by Q and R in


60

x

23


=

23

hours 2 hours.

60

11

60

11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?


Answer: Option BExplanation:Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y.
Then, 4x + 6y =

1

and 3x + 7y =

1

.

8

10

Solving the two equations, we get: x =

11

, y =

1

400

400

1 woman’s 1 day’s work =

1

.

400

10 women’s 1 day’s work =


1

x 10


=

1

.

400

40

Hence, 10 women will complete the work in 40 days.
 A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

A. 
18 days 
B. 
24 days 
C. 
30 days 
D. 
36 days 
Answer: Option A
Explanation:
2(A + B + C)’s 1 day’s work =


1

+

1

+

1


=

15

=

1

.

30

24

20

120

8

Therefore, (A + B + C)’s 1 day’s work =

1

=

1

.

2 x 8

16

Work done by A, B, C in 10 days =

10

=

5

.

16

8

Remaining work =


1 –

5


=

3

.

8

8

A’s 1 day’s work =


1

–

1


=

1

.

16

24

48

Now,

1

work is done by A in 1 day.

48

So,

3

work will be done by A in


48 x

3


= 18 days.


 A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

A. 
4 days 
B. 
6 days 
C. 
8 days 
D. 
18 days 
Answer: Option A
Explanation:
Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.
B’s 1 day’s work =

1

.

12

A’s 1 day’s work =

1

; (2 times of B’s work)

6

(A + B)’s 1 day’s work =


1

+

1


=

3

=

1

.

6

12

12

4

So, A and B together can finish the work in 4 days. 
 A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :

A. 
8 days 
B. 
10 days 
C. 
12 days 
D. 
15 Days 
Answer: Option C
Explanation:
(A + B)’s 1 day’s work =


1

+

1


=

1

.

15

10

6

Work done by A and B in 2 days =


1

x 2


=

1

.

6

3

Remaining work =


1 –

1


=

2

.

3

3

Now,

1

work is done by A in 1 day.

15


2

work will be done by a in


15 x

2


= 10 days.

3

3

Hence, the total time taken = (10 + 2) = 12 days. 
 Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

A. 
3 : 4 
B. 
4 : 3 
C. 
5 : 3 
D. 
Data inadequate 
Answer: Option B
Explanation:
(20 x 16) women can complete the work in 1 day.
1 woman’s 1 day’s work =

1

.

320

(16 x 15) men can complete the work in 1 day.
1 man’s 1 day’s work =

1

240

So, required ratio 




= 4 : 3 (cross multiplied) 

 A and B can do a job together in 7 days. A is 1 times as efficient as B. The same job can be done by A alone in :

Answer: Option B
Explanation:
(A’s 1 day’s work) : (B’s 1 day’s work) =

7

: 1 = 7 : 4.

4

Let A’s and B’s 1 day’s work be 7x and 4x respectively.
Then, 7x + 4x =

1

11x =

1

x =

1

.

7

7

77

A’s 1 day’s work =


1

x 7


=

1

.

77

11



 P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

Answer: Option A
Explanation:
P can complete the work in (12 x 8) hrs. = 96 hrs.
Q can complete the work in (8 x 10) hrs. = 80 hrs.
P’s1 hour’s work =

1

and Q’s 1 hour’s work =

1

.

96

80

(P + Q)’s 1 hour’s work =


1

+

1


=

11

.

96

80

480

So, both P and Q will finish the work in


480


hrs.

11

Number of days of 8 hours each =


480

x

1


=

60

days = 5

5

days.

11

8

11

11


 A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

A. 
4 days 
B. 
6 days 
C. 
8 days 
D. 
12 days 
Answer: Option B
Explanation:
Suppose A, B and C take x,

x

and

x

days respectively to finish the work.

2

3

Then,


1

+

2

+

3


=

1

x

x

x

2

x = 12.
So, B takes (12/2) = 6 days to finish the work. 
 A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

A. 
15 days 
B. 
20 days 
C. 
25 days 
D. 
30 days 
