RD Sharma Solutions for Class 8 Math Chapter 11 Time And Work are provided here with simple step-by-step explanations. These solutions for Time And Work are extremely popular among class 8 students for Math Time And Work Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma Book of class 8 Math Chapter 11 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma Solutions. All RD Sharma Solutions for class 8 Math are prepared by experts and are 100% accurate.

Page No 11.10:

Question 1:

Rakesh can do a piece of work in 20 days. How much work can he do in 4 days?

Answer:

It is given that Rakesh can do a piece of work in 20 days. Rakesh's 1 day's work=120 Rakesh's work for 4 days=420=15Thus, he can do 15th of the work in 4 days.

Page No 11.10:

Question 2:

Rohan can paint 13 of a painting in 6 days. How many days will he take to complete the painting?

Answer:

Rohan can paint 13rd of a painting in 6 days. Time taken by Rohan to complete the painting=6×3 days=18 days.

Page No 11.10:

Question 3:

Anil can do a piece of work in 5 days and Ankur in 4 days. How long will they take to do the same work, if they work together?

Answer:

Time taken by Anil to do the work=5 daysTime taken by Ankur to do the work=4 days Work done by Anil in 1 day=15Work done by Ankur in 1 day=14 Work done by Anil and Ankur in one day=15+14=4+520=920Thus, Anil and Ankur can do the work in 209 days i.e. 229days.

Page No 11.10:

Question 4:

Mohan takes 9 hours to mow a large lawn. He and Sohan together can mow it in 4 hours. How long will Sohan take to mow the lawn if he works alone?

Answer:

Time taken by Mohan to do the work=9 hoursTime taken by Mohan and Sohan to do the work=4 hours Work done by Mohan=19Work done by Mohan and Sohan=14 Work done by Sohan =14-19=9-436=536Thus, Sohan can do the work in 365 hours i.e. 715hours.

Page No 11.10:

Question 5:

Sita can finish typing a 100 page document in 9 hours. Mita in 6 hours and Rita in 12 hours. How long will they take to type a 100 page document if they work together?

Answer:

Time taken by Sita to do the work=9 hoursTime taken by Mita to do the work=6 hoursTime taken by Rita to do the work=12 hoursNow,Work done by Sita=19Work done by Mita=16Work done by Rita=112 Work done by them together =19+16+112=4+6+336=1336Thus, together they can do the work in 3613 hours.

Page No 11.10:

Question 6:

A, B and C working together can do a piece of work in 8 hours. A alone can do it in 20 hours and B alone can do it in 24 hours. In how many hours will C alone do the same work?

Answer:

Time taken by A to do the work=20 hoursTime taken by B to do the work=24 hoursTime taken by A+B+C to do the work=8 hoursNow,Work done by A=120Work done by B=124Work done by A+B+C=18 Work done by C =18-120+124=18-6120+5120=18-11120=15-11120=4120=130Thus, C can do the work in 30 hours.

Page No 11.10:

Question 7:

A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

Answer:

Time taken by A+B to do the work=18 daysTime taken by B+C to do the work=24 daysTime taken by A+C to do the work=36 daysNow,Work done by A+B=118Work done by B+C=124Work done by A+C=136 Work done together =A+B+B+C+A+C=118+124+136=4+3+272=972=18 Work done together =2A+B+C=18 Work done by A+B+C=116Thus, together they can finish the work in 16 days.

Page No 11.10:

Question 8:

A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?

Answer:

Time taken by A+B to do the work=12 daysTime taken by B+C to do the work=15 daysTime taken by A+C to do the work=20 daysNow,Work done by A+B=112Work done by B+C=115Work done by A+C=120 Work done together =A+B+B+C+A+C=112+115+120=5+4+360=1260=15 Work done together =2A+B+C=15 Work done by A+B+C=110 Work done by A alone =A+B+C-B+C=110-115=3-230=130Thus, A alone can do the work in 30 days.

Page No 11.10:

Question 9:

A, B and C can reap a field in 1534 days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?

Answer:

Time taken by A+B+C to do the work=1534 days=634daysTime taken by B+C+D to do the work=14 daysTime taken by C+D+A to do the work=18 daysTime taken by D+A+B to do the work=21 daysNow,Work done by A+B+C=463Work done by B+C+D=114Work done by C+D+A=118Work done by D+A+B=121 Work done by working together =A+B+C+B+C+D+C+A+D+D+A+B=463+114+118+121=463+9+7+6126=463+22126=463+1163=1563 Work done by working together =3A+B+C+D=1563 Work done by A+B+C+D=1563×3=563Thus, together they can do the work in 635 days or 1235 days.

Page No 11.10:

Question 10:

A and B can polish the floors of a building in 10 days. A alone can do 14 th of it in 12 days. In how many days can B alone polish the floor?

Answer:

It is given that A and B can polish the floors of the building in 10 days. Work done by A+B in 1 day=110Now, A alone can do 14th of the work in 12 days. Time taken by A alone to do the complete work = 4×12=48 days Work done by A in 1 day=148Now, work done by B in 1 day =Work done by A+B in 1 day -Work done by A in 1 day=110-148=24-5240=19240Thus, B alone can polish the floor in 24019days or 121219 days.

Page No 11.10:

Question 11:

A and B can finish a work in 20 days. A alone can do 15 th of the work in 12 days. In how many days can B alone do it?

Answer:

It is given that A and B can finish the work in 20 days. Work done by A+B in 1 day =120Now, A alone can do 15th of the work in 12 days. Time taken by A alone to complete the work=5×12=60 days Work done by A in 1 day=160Now, work done by B in 1 day=Work done by A+B in 1 day work-Work done by A in 1 day=120-160=3-160=260Thus, B alone can polish the floor in 602days or 30 days.

Page No 11.10:

Question 12:

A and B can do a piece of work in 20 days and B in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the remaining work?

Answer:

It is given that A can finish the work in 20 days and B can finish the same work in 15 days. Work done by A in 1 day=120Work done by B in 1 day=115 Work done by A+B in 1 day =120+115=3+460=760 Work done by A+B in 2 days=1460=730Remaining work=1-730=2330It is given that the remaining work is done by B. Complete work is done by B in 15 days. 2330 of the work will be done by B in 15×2330 days or 232 days or 1112 days.Thus, the remaining work is done by B in 1112 days.

Page No 11.10:

Question 13:

A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?

Answer:

It is given that A can finish the work in 40 days and B can finish the same work in 45 days. Work done by A in 1 day=140Work done by B in 1 day=145 Work done by A+B in 1 day=140+145=9+8360=17360 Work done by A+B in 10 days=10×17360=1736Remaining work=1-1736=1936It is given that the remaining work is done by B.Complete work is done by B in 45 days. 1936 of the work will be done by B in 45×1936 days or 2334 days.Thus, the remaining work is done by B in 2334 days.

Page No 11.10:

Question 14:

Aasheesh can paint his doll in 20 minutes and his sister Chinki can do so in 25 minutes. They paint the doll together for five minutes. At this juncture they have a quarrel and Chinki withdraws from painting. In how many minutes will Aasheesh finish the painting of the remaining doll?

Answer:

Aasheesh can paint a doll in 20 minutes, and Chinki can do the same in 25 minutes. Work done by Aasheesh in 1 minute=120 Work done by Chinki in 1 minute=125 Work done by them together=120+125=5+4100=9100 Work done by them in 5 minutes=5×9100=920Remaining work=1-920=1120It is given that the remaining work is done by Aasheesh. The work done by Aasheesh in 20 minutes. 1120th work will be done by Aasheesh in 20×1120 minutes or 11 minutes.Thus, the remaining work is done by Aasheesh in 11 minutes.

Page No 11.10:

Question 15:

A and B can do a piece of work in 6 days and 4 days respectively. A started the work; worked at it for 2 days and then was joined by B. Find the total time taken to complete the work.

Answer:

A can do a work in 6 days, and B can do the same work in 4 days. Work done by A in 2 days=26=13Remaining work=1-13=23 Work done by A+Bin 1 day=16+14=2+312=512 512th work is done by A and B in 1 day. 23rd work will be done by A and B in 125×23 days or 85 days. Total time taken=85+2 days=185 days=335 days

Page No 11.10:

Question 16:

6 men can complete the electric fitting in a building in 7 days. How many days will it take if 21 men do the job?

Answer:

It is given that 6 men can complete a job in 7 days. Time taken by 1 man to complete the same job=6×7=42 days Time taken by 21 men to complete the same job=4221=2 days

Page No 11.10:

Question 17:

8 men can do a piece of work in 9 days. In how many days will 6 men do it?

Answer:

It is given that 8 men can complete a job in 9 days. Time taken by 1 man to complete the same job=8×9=72 days Time taken by 6 men to complete the same job=726=12 days

Page No 11.10:

Question 18:

Reema weaves 35 baskets in 25 days. In how many days will she weave 55 baskets?

Answer:

It is given that Reema weaves 35 baskets in 25 days. Time taken by her to weave 1 basket=2535day Time taken by her to weave 55 baskets=2535×55 days=137535 days=2757 days=3927 days

Page No 11.10:

Question 19:

Neha types 75 pages in 14 hours. How many pages will she type in 20 hours?

Answer:

It is given that Neha types 75 pages in 14 hours. Number of pages typed by her in 1 hour=7514 Number of pages typed by her in 20 hours= 7514×20 pages=150014 pages=7507 pages=10717 pagesThus, Neha types 10717 pages in 20 hours.

Page No 11.10:

Question 20:

If 12 boys earn Rs 840 in 7 days, what will 15 boys earn in 6 days?

Answer:

Earnings of 12 boys in 7 days=Rs. 840 Earnings of 12 boys in 1 day=Rs. 8407=Rs. 120 Earnings of 1 boy in 1 day=Rs.12012=Rs. 10 Earnings of 1 boy in 6 days=Rs. 10×6=Rs. 60 Earnings of 15 boys in 6 days=Rs.60×15=Rs. 900

Page No 11.10:

Question 21:

If 25 men earn Rs 1000 in 10 days, how much will 15 men earn in 15 days?

Answer:

Earnings of 25 men in 10 days=Rs.1000 Earnings of 25 men in 1 day=Rs.100010=Rs.100 Earning of 1 man in 1 day=Rs.10025=Rs.4 Earnings of 1 men in 15 days=Rs.15×4=Rs.60 Earnings of 15 men in 15 days=Rs.60×15=Rs. 900



Page No 11.11:

Question 22:

Working 8 hours a day, Ashu can copy a book in 18 days. How many hours a day should he work so as to finish the work in 12 days?

Answer:

If Ashu works for 8 hours daily, he can finish the work in 18 days.If he works for 1 hour daily, he can finish the work in 18×8 days or 144 days. Number of hours he should work daily to finish the work in 12 days=14412=12

Page No 11.11:

Question 23:

If 9 girls can prepare 135 garlands in 3 hours, how many girls are needed to prepare 270 garlands in 1 hour?

Answer:

Number of garlands made by 9 girls in 1 hour =1353=45Number of garlands made by 1 girl in 1 hour =459=5 Number of girls required to make 270 garlands in 1 hour =2705=54.

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Question 24:

A cistern can be filled by one tap in 8 hours, and by another in 4 hours. How long will it take to fill the cistern if both taps are opened together?

Answer:

Time taken by the first tap to fill the cistern=8 hoursTime taken by the second tap to fill the cistern=4 hours Work done by the first tap in 1 hour=18Work done by the second tap in 1 hour=14 Work done by both the taps in 1 hour=18+14=1+28=38Thus, both the taps together will fill the cistern in 83 hours or 223 hours.

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Question 25:

Two taps A and B can fill an overhead tank in 10 hours and 15 hours respectively. Both the taps are opened for 4 hours and they B is turned off. How much time will A take to fill the remaining tank?

Answer:

Pipe A can fill the tank in 10 hours, and pipe B can fill the tank in 15 hours. In 1 hour, A can fill 110th part of the tank.In 1 hour, B can fill 115th part of the tank. In 1 hour, A and B can fill 110+115=3+230=530=16th part of the tank In 4 hours, A and B can fill 16×4=23rd part of the tankRemaining part of the tank=1-23=13Now, A can fill the tank in 10 hours. 13rd part of the tank can be filled by A in (13×10) hours or 103 hours or 313hours.

Page No 11.11:

Question 26:

A pipe can fill a cistern in 10 hours. Due to a leak in the bottom it is filled in 12 hours. When the cistern is full, in how much time will it be emptied by the leak?

Answer:

When there is no leakage, the pipe can fill the cistern in 10 hours.Thus, the pipe can fill 110th part of the cistern in 1 hour.When there is leakage, the pipe can fill the cistern in 12 hours.Therefore, in case of leakage, the pipe can fill 112th part of the cistern in 1 hour.Thus, in one hour, due to leakge, 110-112th or 160th part of the cistern is emptied.Hence, the cistern will be emptied by the leakage in 60 hours.

Page No 11.11:

Question 27:

A cistern has two inlets A and B which can fill it in 12 hours and 15 hours respectively. An outlet can empty the full cistern in 10 hours. If all the three pipes are opened together in the empty cistern, how much time will they take to fill the cistern completely?

Answer:

Time taken by tap A to fill the cistern =12 hoursTime taken by tap B to fill the cistern =15 hoursLet C be the outlet that can empty the cistern in 10 hours.Time taken by tap C to empty the cistern =10 hours Now,Tap A fills 112th part of the cistern in 1 hour.Tap B fills 115th part of the cistern in 1 hour.Tap C empties out 110th part of the cistern in 1 hour.Thus, in one hour, 112+115-110th part of the cistern is filled.We have:112+115-110=10+8-12120=6120=120Thus, in 1 hour, 120th part of the cistern is filled.Hence, the cistern will be filled completely in 20 hours if all the three taps are opened together.

Page No 11.11:

Question 28:

A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 6 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?

Answer:

Time taken by the tap to fill the cistern=4 hours Tap fills 14th part of the cistern in 1 hour.Time taken by the pipe to empty the cistern=6 hours Pipe empties out 16th part of the cistern in 1 hour.Thus, in 1 hour, 14-16th part of the cistern is filled.We have:14-16=6-424=224=112Thus, in 1 hour, 112th part of the cistern is filled.Hence, the cistern will be filled in 12 hours.



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