In this topic, we will teach you how to solve the various kinds of problems based on time and work. We shared set of important points on solving problems based on time and work. The solved question and answers will be helpful in improving your skill.
Time and Work
- If a person can do a work in x days, then work done by him in 1 day is $\frac 1x$
- If a person can do i/n units of work per day, then he can finish the work in n days.
- If A is n times more efficient than B, then A takes $\frac{1}{n}$th of the time taken by B to complete the same amount of work.
- To complete the same amount of work, more men will take less time and fewer men will take more time.
- m1 x d1 x h1 = m2 x d2 x h2
- If the amount of work increases then in the same duration the number of men required to complete the work increases
- If A takes x days to complete a work and B takes y days to complete the same work, then A and B together take $\frac{xy}{x+y}$ days.
Problems
Time and Work - Exercise - Blog
16 questions
- A can complete 3 units of work per day. In how many days can he complete 60 units of work?
- 30 days
- 20 days
- 15 days
- 25 days
Show the answer
Answer: 20 days
Given, A can complete 3 units of work in 1 day
60 units of work can be completed in $\frac{60}{3}$ = 20 days
- A and B can complete a certain amount work in 15 days and 30 days respectively. Working together in how many days can they complete the same amount of work?
- 5 days
- 7 days
- 10 days
- 12 days
Show the answer
Answer: 10 days
In one day A can complete $\frac{1}{15}$ units of work and B can complete $\frac{1}{30}$ units of work.
The amount of work done by A and B together in one day is
$\frac{1}{15} +\frac{1}{30} =\frac{3}{30} =\frac{1}{10}$ units.
Hence A and B can be complete 1/10 units of work in day. They can complete the total work in 10 days working together.
- A printer P1 can print 40000 books in 8 hours while printer P2 can print the same number of books in 10 hours. Working together find the time taken by both the printers to print 45000 books.
- 5 hours
- 6 hours
- 7 hours
- 9 hours
Show the answer
Answer: 5 hours
Number of books printed by P1 in 1 hour = $\frac{40000}{8}$ = 5000 books
Number of books printed by P2 in 1 hour = $\frac{40000}{10}$ = 4000 books
Number of books printed by P1 and P2 together in 1 hour = 5000 + 4000 = 9000 books.
To print 45000 books, both P1 and P2 together take $\frac{45000}{9000}$ = 5 hours
- A and B are working on a job. A takes 10 days to build a wall, while B takes 20 days to demolish the wall completely. If both A and B work together, in how many days can they build the wall completely?
- 25 days
- 15 days
- 30 days
- 20 days
Show the answer
Answer: 20 days
In one day A can build $\frac{1}{10}$ of the wall and B can demolish $\frac{1}{20}$ of the wall.
In one day A and B together can complete, $\frac{1}{10} -\frac{1}{20} =\frac{1}{20}$ of the wall.
Hence A and B together can build the wall completely in 20 days
- A takes 20 days more than B to complete a job. Given that B is two times more efficient than A. Find the time taken by both A and B to complete the same job?
- $\frac{30}{7}$ days
- $\frac{40}{3}$ days
- 15 days
- 12 days
Show the answer
Answer: $\frac{40}{3}$ days
If A takes x days to complete a job, B takes 2x days to complete the same amount of job.
Given 2x-x=20.
Therefore x = 20. Hence A takes 20 days and B takes 2x days i.e 40 days to complete the job.
Hence in 1 day A can do $\frac{1}{20}$ of the work and B can do $\frac{1}{40}$ of the work.
In one day A and B together can do $\frac{1}{20} +\frac{1}{40} =\frac{3}{40}$ units of work.
Then the A and B can together complete the job in $\frac{40}{3}$ days
- A is half as efficient as B and B is two thirds as efficient as C. C can complete a job in 30 days Working together in how many days can A, B and C complete the same amount of work?
- 12 days
- 15 days
- 9 days
- 21 days
Show the answer
Answer: 15 days
In terms of efficiency,
A =$\frac{1}{2}$ B and B =$\frac{2}{3}$ C
Therefore, A =$\frac{1}{2}$ x $\frac{2}{3}$ x C = $\frac{1}{3}$C
Ratio of efficiencies of A , B and C = 1 : 2 : 3
i.e, If C can do 3 units of work per day, then A and B can do 1 and 2 units of work per day respectively.
Together A, B and C can do 6 units of work per day.
Given that C can finish a work in 30 days. Then the total amount of work (assuming C can do 3 units of work / day) is 3 x 30 = 90 units
Together A, B and C can finish the work $\frac{90}{6}$ = 15 days
- A can finish a job in 8 hrs. Working together with B he can finish the same job in 6 hrs. How long does B alone take to finish the job?
- 12 hrs
- 16 hrs
- 20 hrs
- 24 hrs
Show the answer
Answer: 24 hrs
Since A can finish the job in 8hrs, in 1 hour A can finish $\frac{1}{8}$ units of the job.
Let B finish the job in $x$ hours. Then in 1 hour B can finish $\frac{1}{x}$ units of the job.
Given, A and B can together finish the job in 6 hrs. Then in 1 hour they can finish $\frac{1}{6}$ units of the job.
i.e, $\frac{1}{8} + \frac{1}{x} = \frac{1}{6}$
$\frac{1}{x} = \frac{1}{24}$ => x = 24 hours.
Therefore B alone can finish the job in 24hrs.
- A and B together can complete a work in 15 days. If A is twice as efficient as B. Find the time taken by A alone to complete the work?
- 17 days
- 19.5 days
- 22.5 days
- 25 days
Show the answer
Answer: 22.5 days
Given, A is twice as efficient as B. i.e if B can do $x$ units of work per day, then A can complete 2$x$ units of work per day.
Since A and B together complete the work in 15 days, they complete $\frac{1}{15}$ of the work in 1 day.
i.e 2$x$ + $x$ = $\frac{1}{15}$
$x = \frac{1}{45}$
Therefore, A can complete 2$x = \frac{2}{45}$ units of work per day.
A alone can complete the work in $\frac{45}{2}$ = 22.5 days
- If A and B can complete a job in 10 and 15 days respectively. Find the time taken by C alone to complete the job if A, B and C together can complete the job in 4 days.
- 9 days
- 12 days
- 15 days
- 11 days
Show the answer
Answer: 12 days
Since A can complete the job the in 10 days, number of units of work done by A in one day = $\frac{1}{10}$
Since B can complete the job the in 15 days, number of units of work done by B in one day = $\frac{1}{15}$
If C can complete the job the in $x$ days, number of units of work done by C in one day = $\frac{1}{x}$
Since A, B and C together can complete the job the in 4 days, number of units of work done by them in one day = $\frac{1}{4}$
=>$\frac{1}{10} + \frac{1}{15} + \frac{1}{x} = \frac{1}{4}$
$\frac{5}{30} + \frac{1}{x} = \frac{1}{4}$
$x$ = 12 days
C alone can complete the job in 12 days.
- If A and B together can do a work in 40 days. B and C do it in 60 days and A and C can do it in 80 days. Find the time taken by A alone to do the work.
- 96 days
- 80 days
- 45 days
- 74 days
Show the answer
Answer: 96 days
Let the number of units of work done by A in 1 day = a
Let the number of units of work done by B in 1 day = b
Let the number of units of work done by C in 1 day = c
Since A and B can complete the work in 40 days, then number of units of work done by them in 1 day = $\frac{1}{40}$
=> a + b = $\frac{1}{40}$ _______ 1
Since B and C can complete the work in 60 days, then number of units of work done by them in 1 day = 1/60
=> b + c = $\frac{1}{60}$ _______ 2
Since A and C can complete the work in 80 days, then number of units of work done by them in 1 day = 1/80
=> c + a = $\frac{1}{80}$ _______ 3
Using 1, 2 and 3 above
we get a = $\frac{1}{96}$
i.e A can do $\frac{1}{96}$ units of word per days. Hence he can finish the job in 96 days.
- A is twice as efficient as B and B is thrice as efficient as C. If all of them working together can finish the job in 9 days. Find the time taken by A alone to finish the job.
- 10 days
- 12.5 days
- 13.5 days
- 15 days
Show the answer
Answer: 13.5 days
Let the number of units of work done by C per day be $x$. Then,
the number of units of work done by B per day is 2$x$ and
the number of units of work done A per day is 3 x (2$x$) = 6$x$
Given, all of them together can finish the job in 9 days. Then, in one day they can finish $\frac{1}{9}$ units of work.
i.e , 6$x$ + 2$x$ + $x$ = $\frac{1}{9}$
$x = \frac{1}{81}$
i.e In one day A can finish 6$x$ = $\frac{6}{81}$ units of work. Hence A finish the job in $\frac{81}{6} $= 13.5 days
- A alone can complete a job in 24 days. B can do the job in 8 days. A works for 4 days and then is joined by B until the work is complete. Find the total number of days for the work to complete.
- 4 days
- 5 days
- 7 days
- 9 days
Show the answer
Answer: 9 days
Since A can do the job in 24 days, number of units of work done by A in one day = $\frac{1}{24}$
Similarly, number of units of work done by B in one day = $\frac{1}{8}$
Since A works alone for 4 days. Number of units of work done by A in 4 days = 4 x $\frac{1}{24}$ = $\frac{1}{6}$
Remaining amount of work 1-$\frac{1}{6} = \frac{5}{6}$
Let A and B together take $x$ days to complete the remaining work. Then,
$x(\frac{1}{24} + \frac{1}{8}) = \frac{5}{6}$
$x(\frac{4}{24}) = \frac{5}{6}$
$x$ = 5 days.
Therefore total number of days for the work to complete = Number of days taken by A alone + Number of days taken by A and B together to complete the remaining work.
= 4 + 5 = 9 days.
- The time taken by A and B to complete a job is in the ratio 2:3. A and B together can complete the job in 12 days. They together work for 6 days after which B leaves the job. Find the remaining days required to finish the job.
- 13 days
- 15 days
- 12 days
- 9 days
Show the answer
Answer: 15 days
Let A complete 2$x$ units of work per day. Then B complete 3$x$ units of work per day.
Since A and B together can finish the job in 12 days, in one day they complete $\frac{1}{12}$ units of work.
i.e 2$x$ + 3$x$ = $\frac{1}{12}$
$x = \frac{1}{60}$
Hence, A can complete 2$x$ => $\frac{1}{30}$ units of work per day and B can complete 3$x$ => $\frac{1}{20}$ units of work per day.
Since A and B together work for 6 days, number of units of work done in 6 days
= 6 ($\frac{1}{20} + \frac{1}{30}) = \frac{1}{2}$ units.
Remaining work left = $\frac{1}{2}$ units
Time taken to complete the remaining work by A alone => $\frac{\frac{1}{2}}{\frac{1}{30}}$ = 15 days.
- A and B are working on a job. A takes 10 days to build a wall, while B takes 20 days to demolish the wall completely. If both A and B work in alternate days in how many days can they build the wall completely, given that A starts the work?
- 15 days
- 12 days
- 19 days
- 23 days
Show the answer
Answer: 19 days
In one day A can build $\frac{1}{10}$ of the wall and B can demolish $\frac{1}{20}$ of the wall.
Since they work on alternate days and A starts the job,
Amount of the wall built in 2 days = $\frac{1}{10} - \frac{1}{20} = \frac{1}{10}$ of the wall.
Since it takes 2 days to build the $\frac{1}{10}$th of the wall , $\frac{9}{10}$th of the wall is built in 2x9 = 18days.
On the 19th day A builds the remaining $\frac{1}{10}$th of the wall. Thus, the work is done in 19 days.
- A and B together can do a job in 63 days, while B and C can do it in 28 days and A and C can do it in 36 days. If all three work together for 4 days and then B and C leave the job. Find the number of days in A, B and C together can complete the work.
- 12.47 days
- 10.47 days
- 15.74 days
- 16.74 days
Show the answer
Answer: 12.47 days
Let A do 'a' units of work per day and B do 'b' units of work per day and C do 'c' units of work per day.
In one day A and B can do 1/63 units of work => a + b = $\frac{1}{63}$ ______ 1
Similarly, b + c = $\frac{1}{28}$ ______ 2
and a + c = $\frac{1}{36}$ ______ 3
Adding 1, 2 and 3
2 (a + b + c) = 2 ( $\frac{1}{63} + \frac{1}{28} + \frac{1}{36} )$
a + b + c = $\frac{101}{1260}$
In one day A, B and C together can complete $\frac{101}{1260}$ units of work. Hence the number of days taken by A, B and C to complete the work = $\frac{1260}{101}$ = 12.47 days.
- A and B can complete a work in 12 and 15 days respectively. They work together for 4 days and leave the job. The remaining work is completed by C in 8 days. Find the number of days in which C alone can complete the work.
- 20 days
- 15 days
- 25 days
- 30 days
Show the answer
Answer: 20 days
A can complete $\frac{1}{12}$ units of work per day and B can complete $\frac{1}{15}$ units of work per day.
Let c complete $x$ units of work per day.
Number of units of work per day by A and B together = $\frac{1}{12} + \frac{1}{15} = \frac{3}{20} $units of work/day
In 4 days A and B can complete 4 x $\frac{3}{20} = \frac{3}{5}$ units of work
Remaining work = 1 - $\frac{3}{5}$ = $\frac{2}{5}$ units of work.
Since the remaining work of $\frac{2}{5}$ units is completed by C in 8 days,
8$x$ = $\frac{2}{5}$
$x$ = 1/20
Hence C can complete 1/20 units of work per day, which implies that C takes 20 days to complete the work.
