Time and Work Questions Answers

• 1. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.

  1. \begin{aligned} \frac{4}{9} \end{aligned}
  2. \begin{aligned} 2\frac{4}{9} \end{aligned}
  3. \begin{aligned} 3\frac{4}{9} \end{aligned}
  4. \begin{aligned} 4\frac{4}{9} \end{aligned}

  Answer And Explanation

  Answer: Option D

  Explanation:

  In this type of questions, first we need to calculate 1 hours work, then their collective work as,
  
  A's 1 hour work is 1/8
  B's 1 hour work is 1/10
  
  (A+B)'s 1 hour work = 1/8 + 1/10
  = 9/40
  
  So both will finish the work in 40/9 hours
  = \begin{aligned} 4\frac{4}{9} \end{aligned}

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• 2. A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ?

  1. 4 days
  2. 5 days
  3. 6 days
  4. 7 days

  Answer And Explanation

  Answer: Option C

  Explanation:

  (A+B)'s 1 day work = 1/4
  
  A's 1 day work = 1/12
  
  B's 1 day work =
  \begin{aligned}
  \left( \frac{1}{4} - \frac{1}{12} \right) \\
  = \frac{3-1}{12} \\
  = \frac{1}{6} \\
  \end{aligned}
  
  So B alone can complete the work in 6 days

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• 3. A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work ?

  1. 5 days
  2. 6 days
  3. 7 days
  4. 8 days

  Answer And Explanation

  Answer: Option B

  Explanation:

  Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
  So,
  A's 1 day work = 1/10
  B's 1 day work = 1/15
  
  (A+B)'s 1 day work =
  \begin{aligned}
  \left(\frac{1}{10}+\frac{1}{15} \right) \\
  =\left(\frac{3+2}{30} \right) \\
  = \frac{1}{6}
  \end{aligned}
  
  So together they can complete work in 6 days.

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• 4. A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day

  1. 1\5
  2. 1\6
  3. 1\7
  4. 1\8

  Answer And Explanation

  Answer: Option B

  Explanation:

  Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question
  
  So lets solve now,
  A's 1 day work = 1/18
  B's 1 day work = 1/9 [because B take half time than A]
  
  (A+B)'s one day work =
  
  \begin{aligned}
  \left(\frac{1}{18}+\frac{1}{9} \right) \\
  =\left(\frac{1+2}{18} \right) \\
  = \frac{1}{6}
  \end{aligned}
  
  So in one day 1/6 work will be done.

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• 5. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

  1. \begin{aligned} 3\frac{1}{5} min \end{aligned}
  2. \begin{aligned} 3\frac{2}{5} min \end{aligned}
  3. \begin{aligned} 3\frac{3}{5} min \end{aligned}
  4. \begin{aligned} 3\frac{4}{5} min \end{aligned}

  Answer And Explanation

  Answer: Option C

  Explanation:

  Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
  Lets Solve it:
  
  1 minute work done by both the punctures =
  \begin{aligned}
  \left(\frac{1}{9}+\frac{1}{6} \right) \\
  =\left(\frac{5}{18} \right) \\
  \end{aligned}
  
  So both punctures will make the type flat in
  \begin{aligned}
  \left(\frac{18}{5} \right)mins \\
  = 3\frac{3}{5} mins
  \end{aligned}

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• 6. A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work.

  1. 27 days
  2. 54 days
  3. 56 days
  4. 68 days

  Answer And Explanation

  Answer: Option B

  Explanation:

  As per question, A do twice the work as done by B.
  So A:B = 2:1
  Also (A+B) one day work = 1/18
  
  To get days in which B will finish the work, lets calculate work done by B in 1 day =
  \begin{aligned}
  =\left(\frac{1}{18}*\frac{1}{3} \right) \\
  = \frac{1}{54}
  \end{aligned}
  [Please note we multiplied by 1/3 as per B share and total of ratio is 1/3]
  
  So B will finish the work in 54 days

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• 7. A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?

  1. \begin{aligned} 7\frac{1}{2}days \end{aligned}
  2. \begin{aligned} 6\frac{1}{2}days \end{aligned}
  3. \begin{aligned} 5\frac{1}{2}days \end{aligned}
  4. \begin{aligned} 4\frac{1}{2}days \end{aligned}

  Answer And Explanation

  Answer: Option A

  Explanation:

  In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As,
  
  Son's one day work =
  \begin{aligned}
  \left(\frac{1}{3}-\frac{1}{5} \right) \\
  =\left(\frac{5-3}{15} \right) \\
  = \frac{2}{15}
  \end{aligned}
  
  So son will do whole work in 15/2 days
  which is =
  
  \begin{aligned} 7\frac{1}{2}days \end{aligned}

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