Time and Work Problems with Solutions

• 15. 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?

  1. 30 days
  2. 40 days
  3. 50 days
  4. 60 days

  Answer :

  Option B

  Explanation:

  Let 1 man's 1 day work = x
  and 1 woman's 1 days work = y.
  Then, 4x + 6y = 1/8
  and 3x+7y = 1/10
  solving, we get y = 1/400 [means work done by a woman in 1 day]
  
  10 women 1 day work = 10/400 = 1/40
  
  10 women will finish the work in 40 days

• 16. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C

  1. Rs. 300
  2. Rs. 400
  3. Rs. 500
  4. Rs. 600

  Answer :

  Option B

  Explanation:

  C's 1 day's work =
  \begin{aligned}
  \frac{1}{3}- \left(\frac{1}{6} +\frac{1}{8} \right) \\
  =\left(\frac{1}{3} - \frac{7}{24} \right) \\
  = \frac{1}{24} \\
  A:B:C = \frac{1}{6}:\frac{1}{8}:\frac{1}{24} \\
  = 4:3:1 \\
  C's Share = \frac{1}{8}* 3200 \\
  = 400
  \end{aligned}
  If you are confused how we multiplied 1/8, then please study ratio and proportion chapter, for small information, it is the C ratio divided by total ratio.

• 17. 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 :

  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

• 18. 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 :

  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.

• 19. 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 :

  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

• 20. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

  1. 6 days
  2. 7 days
  3. 8 days
  4. 9 days

  Answer :

  Option B

  Explanation:

  1 woman's 1 day's work = 1/70
  1 Child's 1 day's work = 1/140
  5 Women and 10 children 1 day work =
  \begin{aligned}
  \left(\frac{5}{70}+\frac{10}{140}\right) \\
  = \frac{1}{7}
  \end{aligned}
  
  So 5 women and 10 children will finish the work in 7 days.

• 21. 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 :

  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}