Time and Work Problems with Solutions

• 1. 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 :

  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

• 2. 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 :

  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

• 3. 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 :

  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}

• 4. 5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio

  1. 1:2
  2. 1:3
  3. 2:1
  4. 2:3

  Answer :

  Option C

  Explanation:

  Let 1 man 1 day work = x
  1 boy 1 day work = y
  
  then 5x + 2y = 4(x+y)
  => x = 2y
  => x/y = 2/1
  => x:y = 2:1

• 5. A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?

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

  Answer :

  Option A

  Explanation:

  To calculate the answer we need to get 1 man per day work and 1 woman per day work.
  
  Let 1 man 1 day work =x
  and 1 woman 1 days work = y.
  => 6x+5y = 1/6
  and 3x+4y = 1/10
  On solving, we get x = 1/54 and y = 1/90
  
  (9 men + 15 women)'s 1 days work =
  (9/54) + (15/90) = 1/3
  
  9 men and 15 women will finish the work in 3 days
  
  
  

• 6. 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 :

  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}
  

• 7. 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 :

  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