If A can do a piece of work in n days, then A's 1 day's work =

1

.

n

If A's 1 day's work =

1

,

then A can finish the work in n days.

n

1. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

2. 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:

3. 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?

4. 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:

5. 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:

6. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

7. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

8. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

9. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

10. 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?

11. 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?

12. 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?

13. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

14. 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?

15. 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:

Answers:

1. 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

6

=

1

x

2

 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 + B)'s 1 day's work =

1

10

C's 1 day's work =

1

50

(A + B + C)'s 1 day's work =

1

+

1

=

6

=

3

. .... (i)

10

50

50

25

From (i) and (ii), we get: 2 x (A's 1 day's work) =

3

25

 A's 1 day's work =

3

.

50

 B's 1 day's work

1

-

3

=

2

=

1

.

10

50

50

25

If difference of time is 60 days, B takes

3

x 60

= 90 days.

2

A's 1 day's work =

1

30

B's 1 day's work =

1

90

(A + B)'s 1 day's work =

1

+

1

=

4

=

2

30

90

90

45

 A and B together can do the work in

45

= 22

1

days.

5 : 4 :: 20 : x     x =

4 x 20

5

(B + C)'s 1 day's work =

1

+

1

=

7

.

9

12

36

Work done by B and C in 3 days =

7

x 3

=

7

.

36

12

Remaining work =

1 -

7

=

5

.

12

12

Now,

1

work is done by A in 1 day.

24

So,

5

work is done by A in

24 x

5

= 10 days.

Work done by X in 4 days =

1

x 4

=

1

.

20

5

Remaining work =

1 -

1

=

4

.

5

5

(X + Y)'s 1 day's work =

1

+

1

=

8

=

2

.

20

12

60

15

Now,

2

work is done by X and Y in 1 day.

15

So,

4

work will be done by X and Y in

15

x

4

= 6 days.

5

2

5

Then, x + y =

1

and 16x + 44y = 1.

30

Solving these two equations, we get: x =

1

and y =

1

60

60

 B's 1 day's work =

1

.

60

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's 2 day's work =

1

x 2

=

1

.

20

10

(A + B + C)'s 1 day's work =

1

+

1

+

1

=

6

=

1

.

20

30

60

60

10

Work done in 3 days =

1

+

1

=

1

.

10

10

5

Now,

1

work is done in 3 days.

5

 1 woman's 1 day's work =

1

.

320

 1 man's 1 day's work =

1

240

So, required ratio =

1

:

1

= 4 : 3.

1 woman's 1 day's work =

1

70

1 child's 1 day's work =

1

140

(5 women + 10 children)'s day's work =

5

+

10

=

1

+

1

=

1

70

140

14

14

7

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

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