Time & Work
Concept
Time and Work is one of the important methods of aptitude test. Time is a course of duration when a person or a group of people can accomplish a premeditated task. Work is a course of task that is accomplished by a person or group of people. Infact, Time & Work are interrelated with each other. Time is directly proportional to work. The more time is employed, the more work is done with a constant workforce. Incase of expertise of workforce, they works inversely. The more expertise exists, the less time required for a certain task. These types of problems are required to find out how much time a person takes to complete a certain task or how many people should be assigned a particular task to finish the same in a given time limit.
Tips to solve problems on Time & Work:
- Work done = Time Taken x Rate of Work
- Rate of work done = 1/Time Taken to Finish The Work
- Time Taken to Finish the Work = 1/Rate of Work Done
Q. A can do a piece of work in 10 days, and B can do the same work in 15 days. If they work together, how long will it take them to finish the work?
A) 5 days
B) 6 days
The rate of work done by A is 
per day, and the rate of work done by B is 
per day. The rate of work done by both together is 
per day, which is 
per day. Therefore, the time taken by both together to finish the work is 6 days.
per day, and the rate of work done by B is per day. The rate of work done by both together is per day, which is per day. Therefore, the time taken by both together to finish the work is 6 days.
C) 7 days
D) 8 days
Discuss
Q. A can do a piece of work in 12 days, and B can do the same work in 18 days. If they work together for 4 days, what fraction of the work will be left?
A) 
B) 
C)
The rate of work done by A is 
per day, and the rate of work done by B is 
per day. The rate of work done by both together is 
per day, which is 
per day. Therefore, the fraction of work done by both together in 4 days is 
, which is 
. Therefore, the fraction of work left is 
, which is 
.
per day, and the rate of work done by B is per day. The rate of work done by both together is per day, which is per day. Therefore, the fraction of work done by both together in 4 days is , which is . Therefore, the fraction of work left is , which is .
D) 
Discuss
Q. A can do a piece of work in 20 days, and B can do the same work in 30 days. They start working together, but after 5 days, A leaves and B continues working alone. How long will it take B to finish the remaining work?
A) 10 days
B) 15 days
The rate of work done by A is 
per day, and the rate of work done by B is 
per day. The rate of work done by both together is 
per day, which is per day. Therefore, the fraction of work done by both together in 5 days is 
, which is 
. Therefore, the fraction of work left is 
, which is 
. The time taken by B to finish the remaining work alone is 
, which is 17.5 days.
per day, and the rate of work done by B is per day. The rate of work done by both together is per day, which is per day. Therefore, the fraction of work done by both together in 5 days is , which is . Therefore, the fraction of work left is , which is . The time taken by B to finish the remaining work alone is , which is 17.5 days.
C) 20 days
D) 25 days
Discuss
Q. A can do a piece of work in 24 days, and B can do the same work in 36 days. They start working together, but after some time, B leaves and A finishes the remaining work in 10 days. How long did B work with A?
A) 4 days
B) 6 days
C) 8 days
The rate of work done by A is 
per day, and the rate of work done by B is 
per day. The rate of work done by both together is 
per day, which is 
per day. Let x be the time that B worked with A. Then, the fraction of work done by both together in x days is 
. The fraction of work done by A alone in 10 days is 
, which is . The sum of these fractions must be equal to the whole work, which is 1. Therefore, we have: 
Therefore, B worked with A for 8 days.
per day, and the rate of work done by B is per day. The rate of work done by both together is per day, which is per day. Let x be the time that B worked with A. Then, the fraction of work done by both together in x days is . The fraction of work done by A alone in 10 days is , which is . The sum of these fractions must be equal to the whole work, which is 1. Therefore, we have: Therefore, B worked with A for 8 days.
D) 10 days
Discuss
Q. A can do a piece of work in x hours, and B can do the same work in y hours. If they work together, they can finish the work in z hours. What is the value of z in terms of x and y?
A) 
B) 
The rate of work done by A is 
per hour, and the rate of work done by B is 
per hour. The rate of work done by both together is 
per hour. Therefore, the time taken by both together to finish the work is 
hours. Therefore, using algebra, we can simplify: 
Therefore, in terms of x and y, the value of z is 
hours.
per hour, and the rate of work done by B is per hour. The rate of work done by both together is per hour. Therefore, the time taken by both together to finish the work is hours. Therefore, using algebra, we can simplify: Therefore, in terms of x and y, the value of z is hours.
C) 
D) 
Discuss
Q. A machine can produce n units of a product in t hours. How many machines are needed to produce m units of the same product in s hours?
A) 
B) 
C) 
D) 
The rate of production of one machine is 
units per hour. The rate of production of m machines is 
units per hour. The number of machines needed to produce m units in s hours must have a rate of production equal to 
units per hour. Therefore, equating these rates, we get: • 
• Simplifying and rearranging, we get: • 
Therefore, the number of machines needed to produce m units in s hours is s.
units per hour. The rate of production of m machines is units per hour. The number of machines needed to produce m units in s hours must have a rate of production equal to units per hour. Therefore, equating these rates, we get: • • Simplifying and rearranging, we get: • Therefore, the number of machines needed to produce m units in s hours is s.
Discuss
Q. A group of workers can complete a project in d days. If the number of workers is increased by p%, how long will it take them to complete the same project?
A) 
The rate of work done by one worker is 
per day. The rate of work done by a group of workers is proportional to the number of workers. If the number of workers is increased by p%, then the new number of workers is 
times the original number of workers. Therefore, the new rate of work done by the group of workers is 
per day. Therefore, the time taken by the group of workers to finish the same project after increasing their number by p% is 
days. Therefore, using algebra, we can simplify: • • 
• Therefore, in terms of d and p, the time taken by the group of workers to finish the same project after increasing their number by p% is days.
per day. The rate of work done by a group of workers is proportional to the number of workers. If the number of workers is increased by p%, then the new number of workers is times the original number of workers. Therefore, the new rate of work done by the group of workers is per day. Therefore, the time taken by the group of workers to finish the same project after increasing their number by p% is days. Therefore, using algebra, we can simplify: • • • Therefore, in terms of d and p, the time taken by the group of workers to finish the same project after increasing their number by p% is days.
B) 
C) 
D) 
Discuss
Q. A group of workers can complete a project in d days working h hours per day. If they reduce their working hours by r%, how long will it take them to complete the same project?
A) 
B) 
C) 
D) 
Description not available. Let’s discuss.
Discuss
Q. A group of workers can complete a project in d days working h hours per day with an efficiency of e%. If they increase their efficiency by f%, how long will it take them to complete the same project?
A) 
We used the concept of efficiency to solve the problem. Efficiency is the ratio of the actual output to the expected output, expressed as a percentage. For example, if a worker can do a piece of work in 10 days, but he actually does it in 12 days, then his efficiency is 
= 83.33%. The amount of work done by a worker in one hour is proportional to his efficiency. Therefore, if a worker’s efficiency increases or decreases, his work output also increases or decreases accordingly. The amount of work done by one worker in one hour is 
. The amount of work done by a group of workers in one hour is proportional to the number of workers and their efficiency. If they increase their efficiency by f%, then their new efficiency is 
times their original efficiency. Therefore, the new amount of work done by the group of workers in one hour is 
. Therefore, the time taken by the group of workers to finish the same project after increasing their efficiency by f% is 
hours. Therefore, using algebra, we can simplify: • • 
Therefore, in terms of d, h, e, and f, the time taken by the group of workers to finish the same project after increasing their efficiency by f% is hours.
= 83.33%. The amount of work done by a worker in one hour is proportional to his efficiency. Therefore, if a worker’s efficiency increases or decreases, his work output also increases or decreases accordingly. The amount of work done by one worker in one hour is . The amount of work done by a group of workers in one hour is proportional to the number of workers and their efficiency. If they increase their efficiency by f%, then their new efficiency is times their original efficiency. Therefore, the new amount of work done by the group of workers in one hour is . Therefore, the time taken by the group of workers to finish the same project after increasing their efficiency by f% is hours. Therefore, using algebra, we can simplify: • • Therefore, in terms of d, h, e, and f, the time taken by the group of workers to finish the same project after increasing their efficiency by f% is hours.
B) 
C) 
D) 
Discuss
Q. A group of workers can complete a project in d days working h hours per day with an efficiency of e%. If they increase their working hours by g%, and decrease their efficiency by f%, how long will it take them to complete the same project?
A) 
B) 
The amount of work done by one worker in one hour is . The amount of work done by a group of workers in one hour is proportional to the number of workers, their working hours, and their efficiency. If they increase their working hours by g%, and decrease their efficiency by f%, then their new working hours are 
times their original working hours, and their new efficiency is 
times their original efficiency. Therefore, the new amount of work done by the group of workers in one hour is 
. Therefore, the time taken by the group of workers to finish the same project after increasing their working hours by g%, and decreasing their efficiency by f% is 
hours. Therefore, using algebra, we can simplify: • • 
Therefore, in terms of d, h, e, f, and g, the time taken by the group of workers to finish the same project after increasing their working hours by g%, and decreasing their efficiency by f% is hours.
. The amount of work done by a group of workers in one hour is proportional to the number of workers, their working hours, and their efficiency. If they increase their working hours by g%, and decrease their efficiency by f%, then their new working hours are times their original working hours, and their new efficiency is times their original efficiency. Therefore, the new amount of work done by the group of workers in one hour is . Therefore, the time taken by the group of workers to finish the same project after increasing their working hours by g%, and decreasing their efficiency by f% is hours. Therefore, using algebra, we can simplify: • • Therefore, in terms of d, h, e, f, and g, the time taken by the group of workers to finish the same project after increasing their working hours by g%, and decreasing their efficiency by f% is hours.
C) 
D) 
Discuss
