myhelper: RS Aggarwal solution class 8 chapter 13 Time and Work Exercise 13A

Exercise 13A

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Q1 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 1:

Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together?

Answer 1:

$Work done by Rajan in 1 day = \frac{1}{24} Work done by Amit in 1 day = \frac{1}{30} Work done by Amit and Rajan together in 1 day = \frac{1}{24} + \frac{1}{30} = \frac{54}{720} = \frac{3}{40} ∴ They can complete the work in \frac{40}{3} days, i . e ., 13 \frac{1}{3} days if they work together .$

Q2 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 2:

Ravi can do a piece of work in 15 hours while Raman can do it in 12 hours. How long will both take to do it, working together?

Answer 2:

$Time taken by Ravi = 15 h Time taken by Raman = 12 h Work done per hour by Ravi = \frac{1}{15} Work done per hour by Raman = \frac{1}{12} Work done per hour by Ravi and Raman together = \frac{1}{15} + \frac{1}{12} = \frac{9}{60} = \frac{3}{20} ∴ Time taken by Ravi and Raman together to finish the work = \frac{20}{3} h = 6 \frac{2}{3} h$

Q3 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 3:

A and B, working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much time will B alone take to finish it?

Answer 3:

$Time taken by A and B to finish a piece of work = 6 days Work done per day by A and B = \frac{1}{6} Time taken by A alone = 9 days Work done per day by A alone = \frac{1}{9} Work done per day by B = (work done by A and B) - (work done by A) = \frac{1}{6} - \frac{1}{9} = \frac{3 - 2}{18} = \frac{1}{18} ∴ B alone will take 18 days to complete the work .$

Q4 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 4:

Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it?

Answer 4:

$Time taken by Raju = 15 h Work done by Raju in 1 h = \frac{1}{15} Time taken by Raju and Siraj working together = 6 h Work done by Raju and Siraj in 1 h = \frac{1}{6} Work done by Siraj in 1 h = (work done by Raju and Siraj) - (work done by Raju) = \frac{1}{6} - \frac{1}{15} = \frac{5 - 2}{30} = \frac{3}{30} = \frac{1}{10} ∴ Siraj will take 10 h to overhaul the scooter by himself .$

Q5 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 5:

A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. How long will they take to finish it if they work together?

Answer 5:

$Time taken by A to complete the work = 10 days Time taken by B to complete the work = 12 days Time taken by C to complete the work = 15 days Work done per day by A = \frac{1}{10} Work done per day by B = \frac{1}{12} Work done per day by C = \frac{1}{15} Total work done per day = \frac{1}{10} + \frac{1}{12} + \frac{1}{15} = \frac{6 + 5 + 4}{60} = \frac{15}{60} = \frac{1}{4} A, B and C will take 4 days to complete the work if they work together .$

Q6 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 6:

A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?

Answer 6:

$Time taken by A to complete the piece of work = 24 h Work done per hour by A = \frac{1}{24} Time taken by B to complete the work = 16 h Work done per hour by B = \frac{1}{16} Total time taken when A, B and C work together = 8 h Work done per hour by A, B and C = \frac{1}{8} Work done per hour by A, B and C = (work done per hour by A) + (work done per hour by B) + (work done per hour by C) (Work done per hour by C) = (work done per hour by A, B and C) - (work done per hour by A) - (work done per hour by B) = \frac{1}{8} - \frac{1}{24} - \frac{1}{16} = \frac{6 - 2 - 3}{48} = \frac{1}{48} Thus, C alone will take 48 h to complete the work .$

Q7 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 7:

A, B and C working together can finish 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 7:

$A can complete the work in 20 h . Work done per hour by A = \frac{1}{20} B can complete the work in 24 h . Work done per hour by B = \frac{1}{24} It takes 8 h to complete the work if A, B and C work together . Work done together per hour by A, B and C = \frac{1}{8} (Work done per hour by A, B and C) = (work done per hour by A) + (work done per hour by B) + (work done per hour by C) OR (Work done per hour by C) = (work done per hour by A, B and C) - (work done per hour by A) - (work done per hour by B) = \frac{1}{8} - \frac{1}{24} - \frac{1}{20} = \frac{1}{30} ∴ C alone will take 30 h to complete the work .$

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Q8 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 8:

A and B can finish a piece of work in 16 days and 12 days respectively. A started the work and worked at it for 2 days. He was then joined by B. Find the total time taken to finish the work.

Answer 8:

$Time taken by A to complete the work = 16 days Work done per day by A = \frac{1}{16} Time taken by B to complete the work = 12 days Work done per day by B = \frac{1}{12} Work done per day by A and B = \frac{1}{12} + \frac{1}{16} = \frac{4 + 3}{48} = \frac{7}{48} Work done by A in two days = \frac{2}{16} = \frac{1}{8} Work left = 1 - \frac{1}{8} = \frac{7}{8} A and B together can complete \frac{7}{48} of the work in 1 day . Then, time taken to complete \frac{7}{8} of the work = \frac{7}{8} \div \frac{7}{48} = \frac{7}{8} \times \frac{48}{7} = 6 days ∴ Total time taken = 6 + 2 = 8 days .$

Q9 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 9:

A can do a piece of work in 14 days while B can do it in 21 days. They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed?

Answer 9:

$Time taken by A to complete the work = 14 days Work done by A in one day = \frac{1}{14} Time taken by B to complete the work = 21 days Work done by B in one day = \frac{1}{21} Work done jointly by A and B in one day = \frac{1}{14} + \frac{1}{21} = \frac{3 + 2}{42} = \frac{5}{42} Work done by A and B in 6 days = \frac{5}{42} \times 6 = \frac{5}{7} Work left = 1 - \frac{5}{7} = \frac{2}{7} With B working alone, time required to complete the work = \frac{2}{7} \div \frac{1}{21} = \frac{2}{7} \times 21 = 2 \times 3 = 6 days So, the total time taken to complete the work = 6 + 6 = 12 days$

Q10 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 10:

A can do $\frac{2}{3}$ of a certain work in 16 days and B can do $\frac{1}{4}$ of the same work in 3 days. In how many days can both finish the work, working together?

Answer 10:

$A can do \frac{2}{3} work in 16 days So, w ork done by A in one day = \frac{2}{48} = \frac{1}{24} B can do \frac{1}{4} work in 3 days So, w ork done by B in one day = \frac{1}{12} Work done jointly by A and B in one day = \frac{1}{24} + \frac{1}{12} = \frac{1 + 2}{24} = \frac{3}{24} = \frac{1}{8} So, A and B together will take 8 days to complete the work .$

Q11 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 11:

A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by A and B?

Answer 11:

$Time taken by A = 15 days Time taken by B = 12 days Time taken by C = 20 days Work d by A in one day = \frac{1}{15} Work done by B in one day = \frac{1}{12} Work done by C in one day = \frac{1}{20} Work don e in one day by A, B and C together = \frac{1}{15} + \frac{1}{12} + \frac{1}{20} = \frac{4 + 5 + 3}{60} = \frac{12}{60} = \frac{1}{5} Work done by A, B and C together in 2 days = \frac{2}{5} Work remaining = 1 - \frac{2}{5} = \frac{3}{5} Work done by A and B in one day = \frac{1}{15} + \frac{1}{12} = \frac{9}{60} = \frac{3}{20} Time required by A and B to complete the remaining work together = \frac{3}{5} \div \frac{3}{20} = \frac{3}{5} \times \frac{20}{3} = 4 days$

Q12 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 12:

A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?

Answer 12:

$Time needed by A and B to finish the work = 18 days Time needed by B and C to finish the work = 24 days Time needed by C and A to finish the work = 36 days Work done by A and B in one day = \frac{1}{18} Work done by B and C in one day = \frac{1}{24} Work done by C and A in one day = \frac{1}{36} 2 × Work done by A, B and C in one day = \frac{1}{18} + \frac{1}{24} + \frac{1}{36} = \frac{4 + 3 + 2}{72} = \frac{9}{72} = \frac{1}{8} ∴ Work done by A, B and C in one day = \frac{1}{16} So, A, B and C working together will t ake 16 days to complete the work .$

Q13 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 13:

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

Answer 13:

$(A + B) can complete the work in 12 days . (B + C) can complete the work in 15 days . (C + A) can complete the work in 20 days . (A + B)' s 1 day work = \frac{1}{12} (B + C)' s 1 day work = \frac{1}{15} (C + A)' s 1 day work = \frac{1}{20} 2 (A + B + C)' s 1 day work = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5 + 4 + 3}{60} = \frac{12}{60} = \frac{1}{5} (A + B + C)' s 1 day work = \frac{1}{10} A' s 1 day work = \{(A + B + C)' s 1 day work\} - \{(B + C)' s 1 day work\} = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30} A will take 30 days to complete the work, if he works alone .$

Q14 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 14:

Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. If both are opened together in the empty tank, how much time will they take to fill it completely?

Answer 14:

$A can fill a tank in 10 hours . B can fill a tank in 15 hours . Pipe A fills \frac{1}{10} of the tank in one hour. Pipe B fills \frac{1}{15} of the tank in one hour. Part of tank filled by pipes A and B together = \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6} Thus, pipes A and B require 6 hours to fill the tank .$

Q15 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 15:

Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank in 6 hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up completely?

Answer 15:

$Pipe A can fill a tank in 5 hours . Pipe B can empty a full tank in 6 hours . Pipe A fills \frac{1}{5} of the tank in one hour. Pipe B empties \frac{1}{6} of the tank in one hour. Part of the tank filled in one hour using both pipes A and B = \frac{1}{5} - \frac{1}{6} = \frac{6 - 5}{30} = \frac{1}{30} It takes \frac{30}{1} or 30 hours to fill the tank completely .$

Q16 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 16:

Three taps A, B and C can fill an overhead tank in 6 hours, 8 hours and 12 hours respectively. How long would the three taps take to fill the empty tank, if all of them are opened together?

Answer 16:

$Time taken by tap A to fill the tank = 6 hours Time taken by tap B to fill the tank = 8 hours Time taken by tap C to fill the tank = 12 hours A fills \frac{1}{6} of the tank in one hour. B fills \frac{1}{8} of the tank in one hour. C fills \frac{1}{12} of the tank in one hour. Part of the tank filled in one hour using all the three pipes = \frac{1}{6} + \frac{1}{8} + \frac{1}{12} = \frac{4 + 3 + 2}{24} = \frac{9}{24} Time taken by A, B and C together to fill the tank = \frac{24}{9} = \frac{8}{3} = 2 \frac{2}{3} hours$

Q17 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 17:

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

Answer 17:

$Inlet A can fill the cistern in 12 minutes . Inlet B can fill the cistern in 15 minutes . Outlet C empties the filled cistern in 10 minutes . Part of the cistern filled by inlet A in one minute = \frac{1}{12} Part of the cistern filled by inlet B in one minute = \frac{1}{15} Part of the cistern emptied by outlet C in one minute = - \frac{1}{10} (water flows out from C and empties the cistern) Part of the cistern filled in one minute with A, B and C working together = \frac{1}{12} + \frac{1}{15} - \frac{1}{10} = \frac{5 + 4 - 6}{60} = \frac{3}{60} = \frac{1}{20} The time required to fill the cistern with all inlets, A, B and C, open is 20 minutes .$

Q18 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 18:

A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak?

Answer 18:

$A pipe can fill a cistern in 9 hours . Part of the cistern filled by the pipe in one hour = \frac{1}{9} Let the leak empty the cistern in x hours . Part of the cistern emptied by the leak in one hour = - \frac{1}{x} (The leak drains out the water) Considering the leak, t he tank is filled in 10 hours . Part of the tank filled in one hour = \frac{1}{10} Therefore, \frac{1}{9} - \frac{1}{x} = \frac{1}{10} or, \frac{1}{x} = \frac{1}{9} - \frac{1}{10} = \frac{10 - 9}{90} = \frac{1}{90} x = 90$

The leak will empty the filled cistern in 90 hours.

Q19 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Question 19:

Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened and after two hours, pipe A is closed. How much time will B take to fill the remaining part of the tank?

Answer 19:

$Pipe A can fill a cistern in 6 hours . Pipe B can fill a cistern in 8 hours . Part of the cistern filled by pipe A in one hour = \frac{1}{6} Part of the cistern filled by pipe B in one hour = \frac{1}{8} Part of the cistern filled by pipes A and B in one hour = \frac{1}{6} + \frac{1}{8} = \frac{4 + 3}{24} = \frac{7}{24} Part of the cistern filled by pipes A and B in 2 hours = \frac{7}{24} \times 2 = \frac{7}{12} Part of the tank empty after 2 hours = 1 - \frac{7}{12} = \frac{5}{12} Time taken by pipe B to fill the remaining tank = \frac{5}{12} \div \frac{1}{8} = \frac{5}{12} \times 8 = \frac{10}{3} = 3 \frac{1}{3} hours$

RS Aggarwal solution class 8 chapter 13 Time and Work Exercise 13A

Exercise 13A

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Q1 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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Q8 | Ex-13A | Class 8 | RS AGGARWAL | chapter 13 | Time and Work | myhelper

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