TIME AND WORK - SelfStudys

1. If a person can finish a piece of work in n days, then the work done by the person in 1 day is 1 thn

part of the work.

2. If a person completes 1 thn

part of a work in 1 day, then the time taken by the person to finish the work is n days.

3. A cistern is filled with two pipes, one pipe to fill it which is called an inlet and the other pipe to empty it, whichis called an outlet.

4. If an inlet fills a tank in n hours, then it fills 1 thn

part of the tank in 1 hour, i.e., work done by it in 1 hour is 1n .

5. If an outlet empties a full tank in m hours, then it will empty 1 thm

part of the tank in 1 hour, i.e., work done by it is1m

.

Chapter

TIME AND WORK20

Solved Examples

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Ex. 1. 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. Inwhat time can A alone do it ?

Sol. (A + B)’s 1 days’ work = 172

; (B + C)’s 1 days’ work = 1

120; (A + C)’s 1 days’ work =

190

(A + B)’s + (B + C)’s + (A + C)’s 1 days’ work = 1 1 172 120 90

=5 3 4 12 1

360 360 30

2 (A + B + C)’s 1 days’ work = 130 (A + B + C)’s 1 days’ work =

160

A’s 1 days’ work = (A+B+C)’s 1 days’ work – (B + C)’s 1 days’ work

= 1 1 2 1 160 120 120 120

A alone will complete the work in 120 days.

Ex. 2. A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining workin 42 days. In how many days can the two of them complete the work together ?

Sol. A’s 1 days’ work = 1

8020–1Ch

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IIT Foundation Mathematics Class – VIII20–2Ch

A’s 10 days’ work = 10 180 8

Remaining work = 1 718 8

78

of the work is completed by B in 42 days.

The whole work is completed by B in 42 8

7

days = 48 days

B’s 1 days’ work = 148

(A + B)’s 1 days’ work = 1 1 3 5

80 48 240

8 1

240 30

A and B can complete the whole work together in 30 days.Ex. 3. A can do a certain job in 12 days. B is 60% more efficient than A. What is the number of days it takes B to

do the same piece of work ?

Sol. A’s 1 days’ work = 1

12

B’s 1 days’ work = 1.6 16 212 120 15

B shall complete the work in 15 1days 7 days.2 2

Ex. 4. Two men undertook to do a job for Rs 1400. One of them can do it alone in 7 days and the other in 8 days.With the assistance of a boy, they together completed the work in 3 days. How much money did the boyget ?

Sol. First man’s 1 days’ work = 17

Other man’s 1 days’ work = 18

Let the boy complete the whole work in x days. Then

Boys’ 1 days’ work = 1x

Given, 1 1 137 8 x

=1

1 1 1 17 8 3x

1 1 1 13 7 8x

= 56 (24 21)

168

= 56 45 11

168 168

The boy can complete the work in 16811

days.

Ratio of their shares = Ratio of their one days’ work

= 1 1 11: : 24 : 21:117 8 168

The boy’s share = 11 Rs1400 Rs 27556 .


Time and Work 20–3Ch

Ex. 5. 12 children take 16 days to complete a work which can be completed by 8 adults in 12 days. 16 adults startedworking and after 3 days 10 adults left and 4 children joined them. How many days will it take them tocomplete the remaining work ?

Sol. 12 children take 16 days to complete a work.

So, 1 child’s 1 days’ work = 1 1

12 16 192

8 adults take 12 days to complete a work

So, 1 adult’s 1 days’ work = 1 1

8 12 96

16 adults’ 3 days’ work = 1 116 3

96 2


Now (6 adults’ + children’s) 1 days’ work =6 4 16 1

96 192 192 12

1 th

12 of the work is done by them in 1 day

12

of the work will be done in 1 1

1/12 2 days = 6 days.

Ex. 6. 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 work in2 days, then, what is the time taken by 15 men and 20 boys in doing the same type of work ?

Sol. Let 1 man’s 1 days’ work = x and1 boy’s 1 days’ work = y. Then,

6x + 8y = 1

10…(i)

26x + 48y = 12

…(ii)Performing (i) × 6 – (ii), we get

(36x + 48y) – (26x + 48y) = 6 1

10 2

1 11010 100

x x

Putting x = 1

100 in (i) we get

6 18100 10

y

1 6 48

10 100 100y

1200

y

(15 men’s + 20 boys’) 1 days’ work = 15 20 1

100 200 4

15 men and 20 boys shall complete the work in 4 days.

Ex. 7. A, B and C are employed to do a piece of work for Rs 529. A and B together are supposed to do 1913

of the

work and B and C together 823

of the work. What amount should A be paid ?

(a) Rs 315 (b) Rs 345 (c) Rs 355 (d) Rs 375



Sol. (B + C) do 823

of the work

A does 8 15123 23

of the work

Ratio of A’s share to (B + C)’s share = 15 8:23 23

= 15 : 8

A’s share = 15 Rs 529 Rs 345.23

Ex. 8. A contractor undertook to complete a project in 90 days and employed 60 men on it. After 60 days, he found

that 34

of the work has already been completed. How many men can he discharge so that the project may becompleted on time ?

Sol.3 th4

of the work is completed by 60 men in 60 days.

3 th4

of the work is completed by 1 man in (60 × 60) days.

The whole work will be completed 1 man in 460 603

days.

Let the number of men who can complete the remaining 14

of the work in remaining 30 days be x. Then,

1 th4

of the work will be completed by x men in 30 days.

1 th4

of the work will be completed by 1 man in (30 × x) days.

The whole work will be completed by 1 man in (x×30×4) days.

460 603

= x × 30 × 4 x = 40

Number of men who can be discharged = 60 – 40 = 20.Ex. 9. 12 men can complete a work in 30 days by working 9 hours a day. What is the number of men required to

complete 10 times of this work in 24 days by working 5 hours a day ?Sol. 12 men can complete a work in 30 days by working 9 hours a day. 1 man can complete a work in 1 day by working (12 × 30 × 9) hours.

Let the number of men required be x.Then x men can complete 10 times the work in 24 days by working 5 hours a day.

1 man can complete 1 work in 1 day by working 24 510

x hours

12 × 30 × 9 = 24 510

x x = 270 men.

Ex. 10. 10 men working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men workto complete the same work in 12 days.

Sol. To complete the work in 18 days, 10 men work 6 hours a dayTo complete the work in 18 days, 1 man work (10 × 6) hours a dayTo complete the work in a day, 1 man will work (6 × 10 × 18) hours in a day.

(less days, less men, more hours)



To complete the work in 1 day, 15 men will work (6 10 18)

15

hours a day..

To complete the work in 12 days, 15 men will work 6 10 18

12 15

hours a day..

(more days, more men, less hours)= 6 hours a day.

Ex. 11. If 6 persons working 8 hours a day earn Rs 8400 per week, then how much will 9 persons working 6 hoursa day each per week?

Sol . 6 persons working 8 hours a day earn Rs 8400 in a week.

6 persons working 1 hour a day earn Rs 8400

8 in a week.

1 person working 1 hour a day earns Rs 84006 8

in a week.

(less persons, less days, less earnings)

1 person working 6 hours a day earns Rs 8400 6

6 8

in a week.

9 persons working 6 hours a day each Rs 8400 9 6

6 8

in a week.

(more persons, more hours, more earning) = Rs 9450.

Note. In Examples 10 and 11, for more you multiply and for less you divide.

Ex. 12. 24 men can complete a piece of work in 16 days and 18 women can complete the same work in 32 days. 12men and 6 women work together for 16 days. If the remaining work was to be completed in 2 days, howmany additional men would be required besides 12 men and 6 women ?

Sol. 24 men can complete a work in 16 days

1 man’s 1 days’ work = 1

24 1612 men’s 1 day’s work =

12 124 16 32

18 women can complete the work in 32 days

1 woman’s 1 days’ work = 1

18 326 women’s 1 day’s work =

6 118 32 96

(12 men’s + 6 women’s) 16 days’ work = 1 11632 96

3 11696

=

4 21696 3


(12 men’s + 6 women’s) 2 days’ work = 1 1232 96

= 4 12

96 12


3 112 4

1

384 work is done in 1 day by 1 man

1

12 work will be done in 2 days by

1 138412 2

men = 16 men.



1. A can do 1 th5

part of the work in 12 days, B can do

60% of the work in 30 days and C can do 1 rd3

ofthe work in 15 days. Who will complete the workfirst ?(a) A (b) B(c) C (d) A and B both

2. Ten women can complete a piece in 15 days. Sixmen can complete the same piece of work in 10 days.In how many days can 5 women and six men togethercomplete the piece of work ?(a) 15 days (b) 7.5 days(c) 9 days (d) 12.5 days

3. 6 men or 10 boys can complete a piece of work in15 days. If 7 men and x boys complete the samepiece of work in 9 days, then x is equal to(a) 4 (b) 5(c) 6 (d) 7

4. Ramu can complete a job in 8 days. Shyamu cancomplete the same job in 12 days. However, Monu

takes 12 days to complete 3 th4

of the same job.Ramu works for 2 days and then leaves the job. Thenumber of days that will be taken by Shyamu andMonu to complete the balance together is(a) 4.2 (b) 5.1(c) 6.2 (d) 6.5

5. If Ajit can do 14

of the work in 3 days and Sujit can

do 16

of the same work in 4 days, how much willAjit get if both work together and are paid Rs 180in all ?(a) Rs 120 (b) Rs 108(c) Rs 60 (d) Rs 36

6. The work done by a man, a woman and a child arein the ratio 3 : 2 : 1. If the daily wages of 20 men, 30women and 36 children amount to Rs 78, what willbe the wages of 15 men, 21 women and 30 childrenfor 18 weeks ?(a) Rs 7371 (b) Rs 8645(c) Rs 9000 (d) Rs 9500

7. 40 men can do a piece of work in a given time. Ifonly 30 men be engaged, 6 more days are needed tocomplete the work. In how many days can 60 mendo the work ?(a) 9 (b) 10(c) 12 (d) 15

8. A man and a boy working together can complete awork in 24 days. If for the last 6 days, the man alonedoes the work, then it is completed in 26 days. Howlong will the boy take to complete the work alone ?(a) 72 days (b) 20 days(c) 24 days (d) 36 days

9. A and B can do a piece of work in 20 days and 12days respectively. A started the work alone and thenafter 4 days B joined him till the completion of thework. How long did the work last ?(a) 10 days (b) 20 days(c) 15 days (d) 6 days

10. A and B can do a piece of work in 28 and 35 daysrespectively. They began to work together but Aleaves after some time and B completed the remain-ing work in 17 days. After how many days did Aleave ?

(a)2145

days (b) 9 days

(c) 8 days (d) 759

days

11. A alone can do a piece of work in 6 days and Balone in 8 days. A and B undertook to do it forRs 3200. With the help of C, they completed thework in 3 days. How much is to be paid to C ?(a) Rs 375 (b) Rs 400(c) Rs 600 (d) Rs 800

12. If 20 men working 7 hours a day can do a piece ofwork in 10 days, in how many days will 15 menworking 8 hours a day do the same piece of work ?

(a) 15521

days (b) 1123

days

(c) 69

16days (d) 4

15

days

13. 12 cows together eat 756 kg of grass in 7 days. Howmuch grass will be eaten by 15 cows in 10 days ?(a) 1500 kg (b) 1200 kg(c) 1350 kg (d) 1400 kg

14. If 5 spiders can catch 5 flies in 5 minutes, how manyflies can 100 spiders catch in 100 minutes ?(a) 100 (b) 500(c) 1000 (d) 2000

15. 8 men working for 9 hours a day can complete apiece of work in 20 days. In how many days can 7men working for 10 hours a day complete the samepiece of work ?

Question Bank–20(a)



Answers

(a)1202

days (b)3205

days

(c) 21 days (d)4207

days

16. A job can be completed by 12 men in 12 days. Howmany extra days will be needed to complete the job,if 6 men leave after working for 6 days ?(a) 10 days (b) 12 days(c) 8 days (d) 24 days

17. A contractor undertakes to complete a road 360 mlong in 120 days and employs 30 men for thework. After 60 days he finds that only 120 m lengthof the road has been made. How many more menshould he employ so that the work may becompleted in time ?(a) 20 (b) 30(c) 15 (d) 45

18. A wall of 100 metres can be built by 7 men or 10women in 10 days. How many days will 14 menand 20 women take to build a wall of 600 metres ?(a) 15 (b) 20(c) 25 (d) 30

19. Twenty four men can complete a work in sixteendays. Thirty two women can complete the samework in twenty four days. Sixteen men and sixteenwomen started working and worked for 12 days.How many more men are to be added to completethe remaining work in 2 days ?(a) 16 (b) 24(c) 36 (d) 48

20. 12 men and 16 boys can do a piece of work in 5days; 13 men and 24 boys can do it in 4 days. Theratio of the daily work done by a man to that ofa boy is(a) 2 : 1 (b) 3 : 1(c) 3 : 2 (d) 5 : 4

21. Three men, four women and six children cancomplete a work in seven days. A woman doesdouble the work a man does and a child does halfthe work a man does. How many women alonecan complete the work in 7 days ?(a) 7 (b) 8(c) 14 (d) 12

22. A man, a woman and a boy can complete a job in3, 4 and 12 days respectively. How many boys

must assist 1 man and 1 woman to complete the

job in 14

of a day ?(a) 1 (b) 4(c) 19 (d) 41

23. A machine P can print one lakh books in 8 hours,machine Q can print the same number of books in10 hours while machine R can print them in 12hours. All the machines are started at 9 a.m. Whilemachine P is closed at 11 a.m. and the remainingtwo machines complete the work. Approximatelyat what time will the work be finished ?(a) 11 : 30 a.m. (b) 12 noon(c) 12 : 30 p.m. (d) 1 p.m.

24. A takes 5 hours more time than that taken by B tocomplete a work. If working together they cancomplete a work in 6 hours, then the number ofhours that A takes to complete the workindividually is(a) 15 (b) 12(c) 10 (d) 9

25. If x men working x hours per day can do x unitsof a work in x days, then y men working y hoursper day would be able to complete how many unitsof work in y days ?

(a)2

3xy (b)

3

2xy

(c)2

3yx

(d)3

2yx

26. A started a work and left after working for 2 days.Then B was called and he finished the work in 9days. Had A left the work after working for 3days, B would have finished the remaining workin 6 days. In how many days can each of them,working alone finish the whole work ?(a) 5 days, 8.5 days (b) 2.5 days, 7.5 days(c) 5 days, 15 days (d) 3 days, 15 days

27. 15 men can complete a work in 210 days. Theystarted the work but at the end of 10 days, 15additional men, with double efficiency, were in-ducted. How many days in all did they take tofinish the work ?

(a)1722

days (b)3844

days

(c) 7623

days (d) 70 days

1. (c) 2. (b) 3. (b) 4. (b) 5. (a) 6. (a) 7. (c) 8. (a) 9. (a) 10. (c)11. (b) 12. (b) 13. (c) 14. (d) 15. (d) 16. (b) 17. (b) 18. (a) 19. (b) 20. (a)21. (a) 22. (d) 23. (d) 24 (c) 25. (d) 26. (c) 27. (c)



1. (c) A can do 1 th5

part of the work in 12 days

A can do the whole work in (12 × 5) days = 60 days

B can do 60% of the work in 30 days

B can do the whole work in 30 100

60

days

= 50 days

C can do 1 rd3

of the work in 15 days

C can do the whole work in (15 × 3) days= 45 days.

C will complete the work first.2. (b) 10 women can complete a piece of work in 15

days

1 woman can complete in 1 day, 1

10 15 =

1150

part of work6 men can complete the same work in 10 days,

1 man can complete in 1 day, 1

6 10 =

160

part

of the work (6 men’s + 5 women’s) 1 days’ work

= 6 560 150

= 1 1

10 30 =

3 130

= 4

30 =

215

6 men and 5 women can complete the whole

work in 152

= 7.5 days.

3. (b) 6 men = 10 boys 1 man = 106

boys

7 men = 10 76

boys = 353

boys10 boys can complete the work in 15 days

1 boy can complete the work in (10 × 15) days353

x

boys can complete the work in 9 days

1 boy can complete the work in 353

x

×9days.

10 ×15 = 353

x

× 9

9x = 150 – 105 = 45 x = 5.

4. (b) Ramu’s one days’ job = 18

Shyamu’s one days’ job = 1

123 th4

of the job can be done by Monu in 12 days

Whole job can be done by Monu in 4123

days= 16 days

Monu’s one days’ job = 1

16

Ramu’s two days’ job =128

= 14

,

Remaining job = 114

= 34

(Shyamu’s + Monu’s) one days’ job = 1 1

12 16

= 4 348

= 748

748

of the job can be finished by Shyamu and

Monu in 1 day.

34

of the job can be finished by Shyamu and

Monu in 48 3 367 4 7 = 5.1 days.

5. (a) Ajit’s 3 days’ work = 14

Ajit’s 1 days’ work = 1 13 4 =

112

Sujit’s 4 days’ work = 16

Sujit’s 1 days’ work = 1 14 6 =

124

They are paid in the ratio 1 1:

12 24 = 2 : 1

Ajit’s share = 2 Rs 1803 = Rs 120

6. (a) Given, Man : Woman : Child = 3 : 2 :1 M = 3K , W = 2K, C = K, where K is a constant M = 3C , W = 2C 20M + 30 W + 36C = 60C + 60C + 36C = 156C

Hints and Solutions



and 15M + 21W + 30C = 45C + 42C + 30C = 117C

It is given that(20 men + 30 women + 36 children)

= 156 children earn Rs 78 per day

1 child earns Rs 78

156 per day = Rs

12

per day..

(15 men + 21 women + 30 children) = 117

children should get 1Rs 1172

per day,,

i.e., 1Rs 117 18 72

= Rs 7371 in 18

weeks.7. (c) Suppose 40 men can do a piece of work in x

days. Then,

30 men can do the same work in 40

30x

days= (x + 6) days

4x = 3x + 18 x = 18

60 men can do the same work in 18 40

60

days= 12 days.

8. (a) Let 1 man’s 1 days’ work = 1x

and 1 boy’ss

1 days’ work = 1y , Then,

1 1 124x y

Also given , 20 20 6x y x = 1

1 1 620x y x

= 1

1 62024 x

= 1

6x

= 516

6 1

6x x = 36

1y =

1 124 36

= 3 272

= 172 y = 72

The boy will take 72 days to complete the workalone.

9. (a) A’s one days’ work = 120

B’s one days’ work = 1

12

Work done by A in 4 days = 420

= 15

Remaining work = 115

= 45

(A + B)’s 1days’ work =120

+ 1

12 =

215

Number of days to do the remaining work

= 4 25 15 =

4 155 2 = 6 days

Total number of days taken in the completionof work = 6 + 4 = 10 days

10. (c) Supose A left after x days. Then,

Work of (A + B) for x days = 28 35x x

Work of B for 17 days = 1735

17

28 35 35x x = 1

5 4

140x x

= 17135

= 1835

9

140x

= 1835 x =

18 14035 9

= 8 days.

11. (b) Let C does the same work in x days. Then,1 1 136 8 x

= 1 7 124 x

= 13

1x

= 1 73 24 =

124

C will do the same work in 24 days.

The ratio of their one days’ work = 1 1 1: :6 8 24

= 4 : 3 : 1The amount to be paid to C

=1 Rs 3200

(4 3 1)

= Rs 400.

12. (b) 20 men working 7 hours a day can completethe work in 10 days.20 men working 1 hour a day can complete thework in (10×7) days

(Less hours More days)1 man working 1 hour a day can complete thework in (10×7×20) days

(Less men More days)1 man working 8 hours a day can complete the

work in (10 7 20)

8

days

(More hours Less days)15 men working 8 hours a day can complete the

work in 10 7 20

8 15

days

(More men Less days) =353

days = 2113

days



13. (c) 12 cows in 7 days eat 756 kg of grass

12 cows in 1 day eat 7567

kg of grass

(Less days Less grass )

1 cow in 1 day eats 756

12 7

kg of grass

(Less cows Less grass)

1 cow in 10 days eats 756 10 kg7 12

of grass

(More days More grass)

15 cows in 10 days eat 756 10 15 kg7 12

of

grass = 1350 kg(More cows More grass)

14. (d) 5 spiders in 5 minutes catch 5 flies

5 spiders in 1 minute catch 55

flies

1 spider in 1 minute catches 5

5 5flies

1 spiders in 100 minutes catches 5 100

5 5

flies100 spiders in 100 minutes catch

5 100 1005 5

flies = 2000 flies.

15. (d) 8 men working for 9 hours a day can completea piece in 20 days.8 men working for 1 hour a day can completethe work in (20 × 9) days

(Less hours, more days)1 man working for 1 hour a day can completethe work in (20 × 9 × 8) days

(Less men, more days)1 man working for 10 hours a day can complete

the work in 20 9 8

10

days

7 men working for 10 hours a day can complete

the work in 20 9 8

7 10

days =

1447

days

=420 days7

.

16. (b) 12 men can complete in 12 days, 1 work

1 man can complete in 1 day 1

12 12 part of the

work

6 men can complete in 6 days 6 6

12 12

part of the

work =1 th4

of the work.Number of remaining men = 6,

Remaining work = 34

12 men can complete 1 work in 12 days

6 men can complete 34

work in 12 12 3

6 4

=18 days Number of extra days = 18 – 6 = 12 days.

17. (b) Let the number of extra men employed be x.30 men in 60 days complete 120 m long road.

1 man in 1 day will complete 120 m

30 60 long

road.Also, (30 + x) men in 60 days complete 240 mlong road.

1 man in 1 day will complete 240 m

(30+ )×60xlong road.

120

30×60 =

240(30 ) 60x

115

= 4

(30 )x 30 + x = 60 x = 30 30 more men have to be employed.

18. (a) According to question, 10 women = 7 men 20 women = 14 men

14 men + 20 women = 14 men + 14 men = 28 men.

A wall of 100 m is built by 7 men in 10 daysA wall of 100 m is built by 1 man in (10 × 7) days

A wall of 1 m is built by 1 man in 10 7 days100

(less length, less days)A wall of 600 m is built by 1 man in10 × 7 × 600 days

100(more length, more days)

A wall of 600 m is built by 28 men in10 ×7× 600 days

100×28 = 15 days.

19. (b) 1 man’s 1 days’ work = 1

24 16

16 men’s 1days’ work = 16

24 16 =

124




32 24

16 women’s 1 days’ work = 16 1

32 24 48

12 days’ work of (16 men + 16 women)

= 1 11224 48

= 2 1 3 312 1248 48 4


Now (16 men’s + 16 women’s) 2 days’ work

= 1 1224 48

= 1 12

16 8

Remaining work = 1 14 8 =

18

1384

work is done in 1 day by 1 man

18

work will be done in 2 days by 1 13848 2

= 24 men.20. (a) Let 1 man’s 1 days’ work = x and 1 boy’s

1 days’ work = y

Then, 12x + 16y = 15

… (i)

13x + 24y = 14

…(ii)

Multiplying (i) by 3 and (ii) by 2, we get

36 x + 48 y = 35

… (iii)

26x + 48y = 12

… (iv)

Subtracting eqn (iv) from eqn (iii), we get3 1 6 5 1 1105 2 10 10 100

x x

Putting x = 1

100in (i), we get

12 116100 5

y

16y = 1 125 100 =

20 12100

= 8

100 y = 1

200

Required ratio = x : y = 1 1:

100 200= 2 : 1.

21. (a) Let 1 woman’s 1 days’ work = x. Then

1 man’s 1days’ work = 2x

and 1 child’s 1 days’

work = 4x

Given, (3 men’s + 4 women’s + 6 children’s)

1 days’ work =17

3 642 4x xx =

17

6 16 6

4x x x

= 17

28 1

4 7x

149

x

1 woman can alone complete the work in 49 daysTo complete the work in 7 days, number of

women required = 497

= 7.

22. (d) 1 man’s 1 days’ work = 13


1 boy’s 1 days’ work = 1

12Let the number of boys to assist be x. Then,1 13 4 12

x =

11/ 4

4 3

12x

= 4 7 + x = 48

x = 41 boys.

23. (d) (P + Q + R)’s 1 hours’ work = 1 1 18 10 12

= 37

120

Work done by (P + Q + R) in 2 hours = 372

120

= 3760


(Q + R)’s 1 hours’ work = 1 1

10 12

= 1160

1160

of the work is done by (Q + R) in 1 hour

2360

of the work will be done by (Q + R) in

23 1160 60

= 23 1211 11

hours 2 hours.

So, the work will be finished approximately 2hours after 11 a.m., i.e., around 1 p.m.



Solved Examples

24. (c) Let B take x hours to complete a work. Then,A shall take (x + 5) hours to complete the samework.

B’s 1 hours’ work = 1x , AA’s 1 hours’ work =

15x

Given, 1 1

( 5)x x

=

16

5

( 5)x xx x

= 16

22 5

5x

x x

= 16

12x + 30 = x2 + 5x x2 – 7x – 30 = 0 x2 – 10x + 3x – 30 = 0 x(x – 10) + 3(x – 10) = 0 (x – 10) = 0 or (x + 3) = 0

x = 10 or – 3Neglecting negative valuex = 10.

25. (d) x men working x hours in x days = x units work

Then, 1 man working 1 hour in 1 day = 3xx

units

work y men working y hours in y days

= 3 3

3 2xy yx x

26. (c) Suppose A and B do the work in x and y daysrespectively.Now, work done by A in 2 days + work done byB in 9 days = 1

2 9 1x y

Similarly, 3 6x y = 1

Let 1 ax and 1 b

y . Then the equations

become2 9 1a b … (i)3 6 1a b … (ii)

Performing (i) × 2 – (ii) × 3, we get(6a + 12b) – (6a + 27b) = 2 – 3

– 15b = –1 b = 1

15 x = 15

Putting the value of b in (i)

2a + 9 × 1

15 = 1

2a = 315

= 25

a = 15

y = 5.

27. (c) 15 men’s 1 days’ work = 1

210

15 men’s 10 days’ work = 10210

= 121

Remaining work = 1121

= 2021

The additional 15 men’s 1 days’ work = 2

210

= 1

105

These 30 men’s 1 days’ work = 1 1

210 105

= 1 2210

= 3

210 =

170

1 th70

of the work can be done in 1 day

20 th21

of the work can be done in 207021

days

= 2003

days = 2663

days

Total no. of days = 2663

days + 10 days

= 2763

days.

!"!#$ %&' ("$)#*&$

Ex. 1. Two pipes A and B can fill a tank in 15 hours and 30 hours respectively, while a third pipe C can empty thefull tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. In howmuch time will the tank be full?



Sol. Part of the tank filled when all the three pipes are opened for 10 hours

= 1 1 11015 20 25

= 200 150 12010

300

=

230 23300 30

Remaining empty part = 23 7130 30

Part of the tank filled in 1 hour by pipes (A and B) = 1 1 4 3 7

15 20 60 60

760

part is filled in 1 hour

730

part is filled in 2 hours.

Total time to fill the tank = 10 + 2 = 12 hours.Ex. 2. Two pipes A and B can fill a water tank in 20 minutes and 24 minutes respectively and the third pipe C can

empty at the rate of 3 gallons per minute. If A, B and C opened together fill the tank in 15 minutes, thecapacity (in gallons) of the tank is(a) 180 (b) 150 (c) 120 (d) 60

Sol. Part of the tank filled when all the three pipes are opened in 1 minute = 1

15

Part of the tank filled when (A + B) are opened in 1 minute = 1 120 24

= 6 5 11120 120

Part of the tank emptied by C in 1 min. = 11 1 1

120 15 40

Capacity of 140

part of the tank = 3 gallons

Capacity of the tank = (3 × 40) gallons = 120 gallons.

Ex. 3. A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 12

full andboth the taps are opened together, will the tank be filled or emptied? How long will it take before the tank iseither filled completely or emptied completely, as the case may be?

Sol. In one minute, 1 1 1

16 8 16 of the tank can be filled, i.e.,

116

of the whole tank can be emptied.

The whole tank can be emptied in 16 minutes.Since the tank is half full, therefore it will be emptied in 8 minutes.

Ex. 4. Two pipes A and B can fill a cistern in 20 min and 25 min respectively. Both the pipes are opened togetherbut at the end of 5 min, the first is turned off. How long does it take to fill the cistern?

Sol. Let it take x minutes to fill the cistern, then work done by (Pipe A in 5 min. + Pipe B in x min.) = 1

5 120 25

x

25 4 1100

x 25 + 4x = 100 4x = 75 x = 18.75 min

Ex. 5. A cistern can be filled by two pipes in 30 and 40 min respectively. Both the pipes are opened at once, whenthe first pipe must be turned off so that the tank may be just filled in 18 min?

Sol. Let the first pipe be turned off after x minutes, then work done by (First pipe in x min. + Second pipe in18 min.) = 1

18 1

30 40x

4 54 1120x

4x + 54 = 120 4x = 66 x = 66 16.54 min.



Ex. 6. Two pipes can fill a cistern in 30 and 15h respectively. The pipes are opened simultaneously and it is foundthat due to leakage in the bottom, 5h extra are taken for cistern to be filled up. If the cistern is full, in whattime would the leak empty it?

Sol. Part of the cistern filled when the two pipes are opened simultaneously = 1 130 15

1 2 3 130 10 10

, i.e., The two

pipes can fill the cistern together in 10 hours.Together with the leak, the cistern can be filled in (10 + 5) hours = 15 hoursLet the leak take x hours to empty the cistern. Then,

1 1 110 15x

1 1 1 1

10 15 30x

The leak takes 30 hours to empty the cistern.Ex. 7. Pipes A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the

cistern then, what will be the respective times in which A and B will fill the cistern separately.Sol. Suppose pipe A fills the cistern in x min.

Therefore pipe B will fill the cistern in (x + 5) min.

In one minute, pipe A and B can together fill 1 1

5x x

part of the cistern

Given 1 1 1

5 6x x

5 1

( 5) 6x xx x

2

2 5 165

xx

12x + 30 = x2 + 5 x2 – 7x – 30 = 0

x2 – 10x + 3x – 30 = 0 x(x – 10) + 3(x – 10) = 0 (x + 3) (x – 10) = 0 x = –3 or 10

Neglecting negative values x = 10 A and B will the cistern separately in 10 min and 15 min.

Ex. 8. Three pipes A, B and C can fill a tank in 6 min., 8 min, and 12 min. respectively. The pipe C is closed for 4min before the tank is filled. In what time would the tank be fill?

Sol. Let the tank be full in x min. Then,4 1

6 8 12x x x

4 3 2( 4)24

x x x = 1 9x – 8 = 24

9x = 32 x = 539

min.

Ex. 9. Three pipes A, B and C can fill a cistern in 10h, 12h and 15h respectively. First A was opened. After 1 hour,B was opened and after 2 hours from the start of A, C was also opened. Find the time in which the cisternwas just fill.

Sol. Let it take x hours to fill the tank by all the three pipes. Then,Work done by {A in x hours + B in (x – 1) hours + C in (x – 2) hours} = 1

( 1) ( 2) 1

10 12 15x x x 6x + 5(x – 1) + 4(x – 2) = 60

15x – 13 = 60 15x = 73

x = 73 13415 15

= 4 hours + 73 13415 15

× 60 min = 4 hours 52 min.



Ex. 10. Two pipes A and B can fill a tank in 4 hours and 5 hours respectively. If the pipes A and B are turned onalternately for 1 hour each, then what is the time taken to fill the tank?

Sol. When the two pipes are opened alternately for one hour each, part of the tank filled by them in

2 hours = 1 1 94 5 20

Part of the tank filled in 4 hours = 9

10Remaining part =

9 1110 10

This 1 th

10 of the tank has to be filled by pipe A in

4 210 5

hours

The whole tank can be filled in 245

hours.

1. Two pipes A and B can separately fill a cistern in 60minutes and 75 minutes respectively. There is a thirdpipe at the bottom of the cistern to empty it. If allthe three pipes are simultaneously opened, then thecistern is full in 50 minutes. In how much time, thethird pipe alone can empty the cistern?(a) 110 minutes (b) 100 minutes(c) 120 minutes (d) 90 minutes

2. A cistern has a leak which would empty it in 8 hours.A tap is turned on, which admits 6 litres a minuteinto the cistern and it is now emptied in 12 hours.How many litres can the cistern hold?(a) 8000 litres (b) 8400 litres(c) 8640 litres (d) 8650 litres

3. A tank can be filled by two pipes A and B separatelyin 3 hours and 3 hours 45 minutes respectively. Athird pipe C can empty the full tank in 1 hour, whenthe tank was exactly half-filled, all the three pipesare opened. The tank will become empty in(a) 1 hour 15 min (b) 2 hours 30 min(c) 3 hours 15 min (d) 4 hours 10 min

4. A drum can be filled with oil with a supply pipe in40 minutes. Again the full drum can be made empty

by another pipe in 60 minutes. When 23

part of thedrum was filled, the second pipe was opened and itwas stopped after 15 minutes. If the supply pipe isopened now, time required to fill the drum is

(a)1233

min (b)2253

min

(c)1273

min (d)2283

min

5. Two pipes can fill a tank with water in 15 and 12hours respectively and the third pipe can empty itin 4 hours. If the pipes are opened in order at 8, 9

Question Bank–20(b)

and 11 A.M. respectively, the tank will be emptiedat(a) 11 : 40 a.m. (b) 12 : 40 p.m.(c) 1 : 40 p.m. (d) 2 : 40 p.m.

6. Two pipes can fill a cistern in 14 hours and 16 hoursrespectively. The pipes are opened simultaneouslyand it is found that due to leakage in the bottom, 32minutes extra are taken for the cistern to be filledup. If the cistern is full, in what time would the leakempty it?(a) 96 hours (b) 102 hours(c) 106 hours (d) 112 hours

7. A pipe can empty a tank in 40 minutes. A secondpipe with diameter twice as much as that of the firstis also attached with the tank to empty it. The twotogether can empty the tank in

(a) 8 min (b)1133

min

(c) 30 min (d) 38 min8. Three pipes A, B and C can fill a tank in 6 hours.

After working at it together for 2 hours, C is closedand A and B can fill the remaining part in 7 hours.The number of hours taken by C alone to fill thetank is(a) 10 (b) 12(c) 14 (d) 16

9. A large tanker can be filled by two pipes A and B in60 minutes and 40 minutes respectively. How manyminutes will it take to fill the tanker from emptystate if B is used for half the time and A and B fill itfor the other half?(a) 15 minutes (b) 20 minutes(c) 27.5 minutes (d) 30 minutes



Answers

10. Two taps can fill a tank in 20 minutes and 30 min-utes respectively. There is an outlet tap at exactlyhalf level of that rectangular tank which can pumpout 100 litres of water per minute. If the outlet tapis open, then it takes 24 minutes to fill an emptytank. What is the volume of the tank?(a) 1800 litres (b) 1500 litres(c) 1200 litres (d) 2400 litres

11. Two pipes A and B can fill a cistern in 12 min and16 min respectively. Both the pipes are openedtogether for a certain time but due to some

obstruction, the flow of water was restricted to 78

of the full flow in pipe A and 56

of the full in pipe

B. The obstruction, is removed after some time andthe tank is now filled in 3 min from that moment.For how many minutes was the obstruction there?(a) 8 min (b) 3 min(c) 5.6 min (d) 4.5 min

12. Pipes A, B and C are attached to a cistern. A and Bcan fill it in 20 min and 30 min respectively, whileC can empty it in 15 min. If A, B and C are kept in

operation successively for 1 minute each, how soonwill the cistern be filled?(a) 167 min (b) 160 min(c) 166 min (d) 164 min

13. A pipe A can fill a tank in 27 min. Due to develop-

ment of a hole in the bottom of the tank 1

10 of the

water filled by pipe A leaks out. Find the time whenthe tank will be full.(a) 32 min (b) 34 min(c) 36 min (d) 30 min

14. If two pipes are put in operation simultaneously, thetank is filled in 24 min. One pipe fills the tank in 20min faster than the other. How many hours does thefaster pipe take to fill the tank?(a) 60 min (b) 45 min(c) 40 min (d) 30 min

15. Two pipes A and B can fill a cistern in 30 min and40 min respectively. Both the pipes are turned onsimultaneously. When should the second pipe beclosed if the cistern is to be filled in 24 min.(a) 6 min (b) 8 min(c) 10 min (d) 12 min

1. (b) 2. (c) 3. (a) 4. (a) 5. (d) 6. (d) 7. (b) 8. (c) 9. (d) 10. (a)11. (d) 12. (a) 13. (d) 14. (c) 15. (a)

1. (b) Let the third pipe empty the whole cistern in xminutes.

1 1 1 160 75 50x

1 1 1 1 5 4 6 3 1

60 75 50 300 300 100x

The third pipe can empty the cistern in 100minutes.

2. (c) Suppose the cistern holds x litres of water.The tap admits 6 litres of water in 1 minute,i.e., it admits 360 litres of water in 1hour.

x litres of water can be filled in 360

x hours.

The leak would empty the tank in 8 hours.

In one hour, 18

of the tank becomes empty..

If the tap and the leak both are allowed

simultaneously, then the tank becomes emptyin 12 hours, i.e.,

1 360 18 12x

360 1 1 3 2 18 12 24 24x

x = (360 × 24) litres = 8640 litres.3. (a) Part of the tank emptied in 1 hour

= 1 4 9 6 21 13 15 15 15 5

( 3 hr 45 min = 453

3

601544

hrs.)

Time taken to empty the full tank = 1 5

2/5 2

hours Time taken to empty the exactly half filled

tank = 1 52 2 hours =

54

hours = 1 hr 15 min.

Hints and Solutions



4. (a) Part of the drum that can be emptied in 15 min.

by the second pipe = 1 11560 4

After 15 min, part of the drum filled with

oil = 2 1 8 3 53 4 12 12

After 15 min, part of the drum emptied

= 5 71

12 12

Given, the whole drum can be filled in 40 min.

7

12 part of the drum can be filled in

74012

min. = 703

min. = 1233

min.

5. (d) Let the tank be emptied in x hrs after 8 A.M.

Tank filled by first pipe in x hours = 15x

Tank filled by second pipe in (x – 1) hours

= ( 1)

12x

Tank emptied by third pipe in (x – 3) hours

= ( 3)

4x

( 1) ( 3) 0

15 12 4x x x

4 5( 1) 15( 3) 0

60x x x

4x + 5x – 5 – 15x + 45 = 0 – 6x + 40 = 0

x = 40 20 266 3 3 hrs. = 6 hrs. 40 min.

The tank will be emptied at 2:40 p.m.6. (d) Part of the cistern filled by the two pipes in 1

hour = 1 1

14 16

= 15

112 Total time taken by the two pipes and the leak

to fill up the cistern = 112 3215 60

hrs = 8 hrs.

Part of the cistern emptied by the leak in 1 hour

= 1 15 16 15 18 112 112 112

The leak will empty the cistern in 112 hours.

7. (b) A pipe with double the diameter can empty atank in half the time, i.e., in 20 min.

Part of the tank emptied by the two pipes

together = 1 1 1 2 340 20 40 40

The tank will be emptied by the two pipes

together in 403

min. = 1133

min.

8. (c) Part of the tank filled by (A + B + C) in 2 hours

= 1 126 3

Remaining part = 1 213 3

2 rd3

of the tank is filled by (A + B) in 7 hours.

The whole tank is filled by (A + B) in 372

hours = 212

hours

Part of the tank filled by C in 1 hour= Part of the tank filled by (A + B + C) in 1 hour

– Part of the tank filled by (A + B) in 1 hour

= 1 2 3 16 21 42 14

C can fill the whole tank in 14 hours.9. (d) Let the total time taken to fill the tank be x

minutes.Then,work by B in half hour + work done by

(A + B) in half hour = 1

1 1 1 140 2 60 40 2

x x

180 48

x x

3 5 1

240x x

8x = 240 x = 30 min.10. (a) Part of the tank that can be filled by the two

filler taps =1 130 20

2 3 5 160 60 12

The two taps can fill the tank in 12 minutes. Half of the tank will be filled in 6 minutes. The time taken by the remaining half of the

tank to be filled when the outlet pipe is open= (24 – 6) min = 18 min.



Part of that half of the tank that can be emptied

in 1 hour = 1 1 16 18 9

Time taken to empty half of the cistern= 9 minutes

Capacity of the tank = 100 × 9 × 2 = 1800 litres.11. (d) Let the obstruction remain for x minutes only.

Part of cistern filled in x minutes + Part of cis-tern filled in 3 minutes = cistern filled

7 58 12 6 16

x x +

3 3 112 16

12 7 196 16

x

12 996 16

x

x = 9 96

16 12

= 4.5 min.

12. (a) Work done in 3 min. = 1 1 1 120 30 15 60

Work done in 3 × 55 = 165 min = 5560

Remaining tank = 55 5 1160 60 12

Now its A’s turn, 120

part of the tank is filledby A in 1 min.

Since there is still 1 1 1

12 20 30

tank to be

filled, which will be filled by B in 1 min.Therefore, required time = (165 + 2) = 167 min.

13. (d) In one minute 127

part of the tank is filled. Due

to leak every minute, 1 1 1

10 27 270 part of the

tank leaks out. Hence the whole tank will beemptied in 270 min by the leak.So, resultant work by pipe and leak in one min.

= 1 1 9 127 270 270 30

The tank will be filled in 30 min.14. (c) Let one pipe take x minutes to fill the tank, then

the other will take (x + 20) minutes.

Given, 1 1 1

20 24x x

220 1

2420x xx x

(2x + 20)24 = x2 + 20x

x2 – 28x – 480 = 0 x2 – 40x + 12x – 480 = 0 x(x – 40) + 12(x – 40) = 0 (x – 40) (x +12) = 0 x = 40 or –12

Neglecting negative values x = 40 min.15. (a) Let the second pipe be closed after x minutes.

Then, 24 130 40

x

96 3 1

120x 3x = 120 – 96 = 24 x = 6 min.

1. A and B working separately can do a piece of workin 9 days and 12 days respectively. If they work for10 days alternately. A beginning, in how many daysthe work will be completed?

(a) 11 days (b) 111 days2

(c) 110 days4

(d) 110 days2

2. A, B and C complete a piece of work in 25, 20 and24 days respectively. All work together for 2 daysand then A and B leave the work. C works for next

385 days and then A along with D joins C and all

finish the work in next three days. In how manydays D alone can complete the whole work?

(a) 22 days (b) 121 days2

(c) 23 days (d) 122 days2

3. 75 boys do a piece of work in 24 days. How manymen will finish double the work in 20 days whenone days’ work of 2 men is equal to one days’ workof 3 boys?(a) 100 men (b) 150 men(c) 120 men (d) 80 men

4. It takes 8, 12 and 16 days for X, Y and Z respectivelyto complete a work. How many days will it take tocomplete the work if X works on it for 2 days, andthen Y works on it for until 25% of the work is leftfor Z to do, and then Z complete the work?(a) 10 days (b) 12 days(c) 8 days (d) 14 days

Self Assessment Sheet–20



Answers

5. 12 children take 16 days to complete a work whichcan be completed by 8 adults in 12 days. 16 adultsstarted working and after 3 days 10 adults left and 4children joined them. How may days will it takethem to complete the remaining work?(a) 6 (b) 8(c) 4 (d) 3

6. 40 men take 8 days to earn Rs 2000. How manymen will earn Rs 200 in 2 days?(a) 10 (b) 1(c) 8 (d) 20

7. A cistern which could be filled in 9 hours takes onehour more to be filled owing to a leak in its bottom.If the cistern is full, in what time will the leak emptyit?(a) 19 hours (b) 1 hours

(c) 90 hours (d) 10 hours9

8. A swimming pool is fitted with three pipes withuniform flow. The first two pipes operatingsimultaneously fill the pool in the same time as thattaken by the third pipe alone. The second pipe fillsthe pool 5 hours faster than the first pipe and 4 hours

slower than the third pipe. Find the time requiredby the third pipe to fill the pool.(a) 10 hours (b) 6 hours(c) 16 hours (d) 5 hours

9. Two pipes A and B can fill a cistern is 12 minutesand 15 minutes respectively but a third pipe C canempty the full tank in 6 minutes. A and B are keptopen for 5 minutes in the beginning and then C isalso opened. In what time will the cistern beemptied?(a) 30 min (b) 33 min(c) 37.5 min (d) 45 min

10. A tap can fill a bath in 20 minutes and another tapcan fill it in 30 minutes. Amit opens both the tapssimultaneously. When the both should have beenfull, he finds that the waste pipe was open. He thencloses the waste pipe and in another 4 minutes thebath is full. In what time would the waste pipe emptyit?(a) 35 min (b) 38 min(c) 36 min (d) 39 min

1. (c) 2. (d) [Hint. Total work completed by A, B, C and D = 1 Work completed by ( A in 5 days + B in 2 days + C

in 3(2 8 3)5

days + D in 3 days) 5 2 68 3 125 20 5 24

x

]

3. (c) 4. (b) 5. (a) 6. (b) 7. (c) 8. (b) 9. (d)

10. (c) [Hint. Bath filled by both the taps in 1 min = 1 1 120 30 12

The waste pipe empties as much bath in 12 minutes as the other two taps together can fill in 4 minutes.

Bath filled in 4 min =1 14

12 3 . Now find the reqd. time.]


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TIME AND WORK - SelfStudys