TIME AND WORK

Time and work problems are a common type of quantitative aptitude questions in competitive exams. These problems assess a candidate's ability to understand and apply the concepts of work, time, and efficiency

Time and Work problems are a fundamental part of the Quantitative Aptitude section in many competitive exams like SSC, Bank PO, Railway Recruitment Boards (RRBs), etc. These problems test your ability to understand and apply basic mathematical concepts to real-life scenarios involving work done by individuals or groups over time

Time and Work – Introduction and Concept

Time and work problems are a common type of quantitative aptitude questions that assess a person's ability to understand and apply the concepts of work, time, and efficiency. These problems involve calculating the amount of work done by individuals or groups working together over a certain period.

In these problems, the relationship between the amount of work, the time taken to complete the work, and the efficiency of individuals or groups is explored. Efficiency is the rate at which work is done. The basic formula relating work, time, and efficiency is:

$Work = Efficiency \times Time$

This formula can be rearranged to find time or efficiency depending on what information is given in the problem.

Basic Concepts:

Work (W): Work is the amount of a task or job that needs to be completed. It is often measured in terms of units.
Time (T): Time is the duration required to complete a certain amount of work. It is usually measured in days, hours, or minutes.
Efficiency (E): Efficiency is the rate at which work is done. It is often expressed as the fraction of work completed per unit of time.

Work Formula:

This formula expresses the relationship between work, efficiency, and time. It can be rearranged to find time or efficiency depending on the given information.
Efficiency Formula:

Efficiency is the rate at which work is done. It represents the amount of work completed per unit of time.
Time Formula:

Time is the duration or amount of time required to complete a certain amount of work. This formula helps calculate the time needed based on efficiency and work.
Combined Efficiency Formula (When A and B work together): $Combined Efficiency (A and B) = E_{A} + E_{B}$

When two individuals (A and B) work together, their combined efficiency is the sum of their individual efficiencies.
Combined Efficiency Formula (When A, B, and C work together): $Combined Efficiency (A, B, and C) = E_{A} + E_{B} + E_{C}$

Similarly, when three individuals (A, B, and C) work together, their combined efficiency is the sum of their individual efficiencies.
Reciprocal Relationship between Time and Efficiency: $Time \times Efficiency = Work$

This formula highlights the reciprocal relationship between time and efficiency. The product of time and efficiency is equal to the amount of work done

Time & Work – Sample Questions

Level 1 - Beginner:

John can paint a fence in 6 hours. Sarah can paint the same fence in 8 hours. How long would it take for them to paint the fence together?
A machine can fill a pool with water in 10 hours. If another machine is added, they can fill the pool in 4 hours. How long would it take the additional machine to fill the pool alone?
Lisa can type 50 words per minute. How many words can she type in 2 hours?

Answers

John and Sarah can paint the fence in 4 hours because their rates added together give you the combined rate: 1/6 + 1/8 = 7/24 per hour. Therefore, the total time taken is 24/7 hours or 3 3/7 hours.
The additional machine alone would take 20 hours to fill the pool. We know the combined rate of both machines is 1/4 of the pool per hour. Since one machine takes 10 hours, its rate is 1/10 per hour. Subtracting this from the combined rate gives us the rate of the second machine: 1/4 - 1/10 = 3/20 per hour. Finally, divide the total work (1 pool) by the individual rate to find the time: 1 pool / (3/20 per hour) = 20 hours.
Lisa can type 6,000 words in 2 hours. Since she types 50 words per minute, multiply this by the number of minutes in 2 hours: 50 words/minute * 120 minutes/hour * 2 hours = 6,000 words.

Level 2 - Intermediate:

A team of construction workers can build a house in 15 days. If 5 more workers join the team, they can build the house in 10 days. How many workers were in the original team?
John and Mary can paint a room together in 4 hours. If John can paint the room alone in 6 hours, how long would it take Mary to paint the room alone?
A factory produces 100 bicycles in 5 hours. If the factory increases its production rate by 20%, how many bicycles can it produce in 4 hours?

Answers

The original team had 10 workers. Let x be the number of workers in the original team. When 5 more workers join, the combined rate increases, meaning they can build the house in fewer days: (x + 5)/10 = 1/15. Solve for x: 15x + 75 = 10x. x = 30.
Mary can paint the room alone in 12 hours. We know John and Mary together can paint the room in 4 hours, so their combined rate is 1/4 of the room per hour. John's individual rate is 1/6 of the room per hour. Subtract John's rate from the combined rate to find Mary's rate: 1/4 - 1/6 = 1/12 per hour. Finally, divide the total work (1 room) by Mary's individual rate: 1 room / (1/12 per hour) = 12 hours.
The factory can produce 120 bicycles in 4 hours. A 20% increase in production rate means the new rate is 1.2 times the original rate. Multiply the original production rate (100 bicycles/5 hours) by 1.2: 100 bicycles/5 hours * 1.2 = 120 bicycles/5 hours. Finally, adjust the production for 4 hours: 120 bicycles/5 hours * 4 hours = 96 bicycles

Level 3 - Advanced:

Three pipes of different diameters can fill a tank with water. Pipe A can fill the tank in 6 hours, pipe B can fill the tank in 8 hours, and pipe C can fill the tank in 12 hours. If all three pipes are open, how long will it take to fill the tank?
A car travels 200 km at a constant speed. The first 100 km are covered in 2 hours. How long will it take to cover the remaining 100 km?
John invests $10,000 in a business and Mary invests $15,000. They agree to share the profits in proportion to their investments. If the business makes a profit of $2,500 in 1 month, how much will each person receive?

Answers

7. Three Pipes:

The key here is to understand the combined rate of all three pipes. Each pipe's rate represents the fraction of the tank they can fill in one hour.

Pipe A's rate: 1/6 tank/hour
Pipe B's rate: 1/8 tank/hour
Pipe C's rate: 1/12 tank/hour

Combine these rates to find the overall rate:

Combined rate = 1/6 + 1/8 + 1/12 = 7/24 tank/hour

This means if all three pipes are open, they can fill the entire tank in 24/7 hours, which is roughly 3.43 hours.

8. Car Trip:

Since the car's speed is constant, we can use the information about the first half of the trip to find the speed.

Distance covered = 100 km
Time taken = 2 hours

Therefore, the speed is 100 km / 2 hours = 50 km/hour.

To find the time needed to cover the remaining 100 km, simply divide the distance by the speed:

Time remaining = 100 km / 50 km/hour = 2 hours

So, it will take another 2 hours for the car to cover the remaining 100 km.

9. Profit Sharing:

First, calculate the total percentage each person owns in the business based on their investment:

TIME AND WORK

TIME AND WORK

Time and Work – Introduction and Concept

Time & Work – Sample Questions

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