Time and Work Questions Answers

• 8. A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many days ?

  1. \begin{aligned} 6\frac{1}{2}days \end{aligned}
  2. \begin{aligned} 7\frac{1}{2}days \end{aligned}
  3. \begin{aligned} 8\frac{3}{5}days \end{aligned}
  4. \begin{aligned} 9\frac{3}{5}days \end{aligned}

  Answer And Explanation

  Answer: Option D

  Explanation:

  In this question we having, A's work, B's work and A+B+C work. We need to calculate C's work.
  We can do it by,
  (A+B+C)'s work - (A's work + B's work).
  
  Let's solve it now:
  
  C's 1 day work =
  \begin{aligned}
  \frac{1}{4}- \left(\frac{1}{16} +\frac{1}{12} \right) \\
  =\left(\frac{1}{4} - \frac{7}{48} \right) \\
  
  = \frac{5}{48}
  \end{aligned}
  
  So C can alone finish the job in 48/5 days,
  Which is =
  \begin{aligned} 9\frac{3}{5}days \end{aligned}

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• 9. To complete a work A and B takes 8 days, B and C takes 12 days, A,B and C takes 6 days. How much time A and C will take

  1. 24 days
  2. 16 days
  3. 12 days
  4. 8 days

  Answer And Explanation

  Answer: Option D

  Explanation:

  A+B 1 day work = 1/8
  B+C 1 day work = 1/12
  A+B+C 1 day work = 1/6
  
  We can get A work by (A+B+C)-(B+C)
  And C by (A+B+C)-(A+B)
  
  So A 1 day work =
  \begin{aligned}
  \frac{1}{6}- \frac{1}{12} \\
  = \frac{1}{12}
  \end{aligned}
  
  Similarly C 1 day work =
  \begin{aligned}
  \frac{1}{6}- \frac{1}{8} \\
  = \frac{4-3}{24} \\
  = \frac{1}{24}
  \end{aligned}
  
  So A and C 1 day work =
  
  \begin{aligned}
  \frac{1}{12} + \frac{1}{24} \\
  = \frac{3}{24} \\
  = \frac{1}{8}
  \end{aligned}
  
  So A and C can together do this work in 8 days

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• 10. A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

  1. 40 days
  2. 35 days
  3. 30 days
  4. 25 days

  Answer And Explanation

  Answer: Option C

  Explanation:

  Suppose B takes x dáys to do the work.
  As per question A will take
  \begin{aligned}
  2* \frac{3}{4} * x = \frac{3x}{2}days
  \end{aligned}
  
  (A+B)s 1 days work= 1/18
  1/x + 2/3x = 1/18 or x = 30 days

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• 11. A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in

  1. 15 days
  2. 10 days
  3. 9 days
  4. 8 days

  Answer And Explanation

  Answer: Option A

  Explanation:

  Ratio of times taken by A and B = 1:3
  Means B will take 3 times which A will do in 1 time
  
  If difference of time is 2 days, B takes 3 days
  If difference of time is 10 days, B takes (3/2) * 10 =15 days

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• 12. A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in

  1. 5 days
  2. 6 days
  3. 7.5 days
  4. 8.5 days

  Answer And Explanation

  Answer: Option C

  Explanation:

  B's 5 days work =
  \begin{aligned}
  \frac{1}{10}*5 = \frac{1}{2} \\
  \text{Remaining work =} 1-\frac{1}{2} \\
  = \frac{1}{2} \\
  
  \text{A can finish work =}15*\frac{1}{2} \\
  = 7.5 days
  
  \end{aligned}
  

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• 13. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the work ?

  1. 10 hours
  2. 12 hours
  3. 16 hours
  4. 18 hours

  Answer And Explanation

  Answer: Option B

  Explanation:

  Work done by A in 1 hour = 1/4
  
  Work done by B and C in 1 hour = 1/3
  
  Work done by A and C in 1 hour = 1/2
  
  Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12
  
  Work done by B in 1 hour = (7/12)–(1/2) = 1/12
  
  => B alone can complete the work in 12 hour

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• 14. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?

  1. \begin{aligned} 35\frac{1}{2} \end{aligned}
  2. \begin{aligned} 36\frac{1}{2} \end{aligned}
  3. \begin{aligned} 37\frac{1}{2} \end{aligned}
  4. \begin{aligned} 38\frac{1}{2} \end{aligned}

  Answer And Explanation

  Answer: Option C

  Explanation:

  Work done by A in 20 days = 80/100 = 8/10 = 4/5
  
  Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
  
  Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
  
  Work done by A and B in 1 day = 1/15 ---(2)
  
  Work done by B in 1 day = 1/15 – 1/25 = 2/75
  
  => B can complete the work in 75/2 days = 37 (1/2) days

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