Time and Work Problems with Solutions

• 8. 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
  5. Lipsticks
  6. Nail Enamels
  7. Shampoos
  8. Conditioners

  Answer :

  Option

  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

• 9. A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the wotk were ?

  1. \begin{aligned} 14\frac{2}{3}kmph \end{aligned}
  2. \begin{aligned} 15\frac{2}{3}kmph \end{aligned}
  3. \begin{aligned} 16\frac{2}{3}kmph \end{aligned}
  4. \begin{aligned} 17\frac{2}{3}kmph \end{aligned}
  5. Z
  6. X
  7. Y
  8. X and Z

  Answer :

  Option

  Explanation:

  Work done by A in l0 days = (1/25) *10 = 2/5
  Remaining work = 1 - (2/5) = 3/5
  (A+B)s 1 days work = (1/25) + (1/20) = 9/100
  
  9/100 work is done by them in 1 day.
  hence 3/5 work will be done by them in (3/5)*(100/9)
  = 20/3days.
  
  Total time taken = (10 + 20/3) = 16*(2/3) days

• 10. A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed in

  1. \begin{aligned} 13\frac{1}{4} \end{aligned}
  2. \begin{aligned} 13\frac{1}{2} \end{aligned}
  3. \begin{aligned} 13\frac{3}{4} \end{aligned}
  4. \begin{aligned} 13\frac{4}{4} \end{aligned}

  Answer :

  Option C

  Explanation:

  A's 1 day work = 1/16
  B's 1 day work = 1/12
  
  As they are working on alternate day's
  So their 2 days work = (1/16)+(1/12)
  = 7/48
  
  [here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]
  
  Work done in 6 pairs = 6*(7/48) = 7/8
  
  Remaining work = 1-7/8 = 1/8
  
  On 13th day it will A turn,
  then remaining work = (1/8)-(1/16) = 1/16
  
  On 14th day it is B turn,
  
  1/12 work done by B in 1 day
  
  1/16 work will be done in (12*1/16) = 3/4 day
  
  So total days =
  \begin{aligned} 13\frac{3}{4} \end{aligned}
  
  It may be a bit typical question, but if are not getting it in first try then give it a second try. Even not, then comment for explanation for this. We will be happy to help you.
  

• 11. 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 :

  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

• 12. 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 :

  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.

• 13. 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 :

  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}

• 14. 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 :

  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}