Solved Time and Work Problems, Tricks | Time and Work Questions and Answers

# Solved Time and Work Problems, Tricks | Time and Work Questions and Answers

Are you preparing for competitive exams? If yes, then you must check this article to know Time & Work shortcuts and Tricks. Understand Time and Work Quantitative Aptitude Questions and Formula. Check shortcuts mentioned here and practice them accurately to solve those questions in a limited time.

## Time & Work Quick Tricks

Solving aptitude questions in a limited time is really a great blessing for the candidates preparing for competitive exams. It can only be possible through regular practice. We are providing a few solved example questions, easy steps, and shortcuts to prepare for the exam. Aptitude is actually easy and interesting if you know shortcuts and steps to solve the problem. You have to follow a few tips and tricks to solve Time and Work Questions.

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This section of aptitude is tricky when compared with other sections and you need to practice more. Also, make your basics strong so that you can solve many problems in less time. Time problems deal with the efficiency of an individual or group or the time taken to complete the work in time. Work is the effort put in to accomplish the task or produce a deliverable.

### The relation between Efficiency and Time Formulas

1. If X and Y can together complete a workpiece in A days, X and Y in B days, and Z and X in C days, then
a) X, Y, and Z working together will complete the work in (2ABC/AB+BC+CA) days.
b) X alone will complete the work in (2ABC/AB+BC – CA) days.
c) Y alone will complete the work in (2ABC/CA+AB – BC) days.
d) Z alone will complete the work in (2ABC/CA+BC – AB) days.
2. If X and Y working together can complete a piece of work in A days and Y is k times efficient than X, then the time taken by X working alone to finish the piece of work is (k+1)A and Y working alone to finish the work is (k+1/k)A
3. Suppose X can finish a job in A days and Y is k times efficient than X, then the time taken by both X and Y working together to finish the work is A/(1+k).
4. If X does 1/nth of a job in an hour, then to finish the full job X will take n*a hours
5. If 1/n of a job is done by A in one day, then X will take n days to finish the full work.
6. Suppose X, Y, and Z, while working alone, can finish work in A, B, and C days respectively, then they will work together to finish the work in ABC/(AB+BC+CA) days.
7. If X can do a piece of work in A days and Y can do the same work in B days, then both of them together will finish the same work in AB/(A+B) days.

### Formulas on Time and Work

There are various approaches to solve efficiency and work problems. We are going to discuss those approaches with you here. Before starting the practice know all the approaches and formulae and be perfect in that.

#### 1st Approach: The Chocolate Method

To make calculations more instinctive, the job can be supposed as chocolates to be consumed instead of units of work to be finished. We consider the LCM of all the “total no of days” given in the question. This is done with the goal that the work will be multiple of “number of days” and hence calculating efficiency will be simpler.

Example:

Question: If X can do work in 9 days and Y can do the same work in 18 days, in how many days can they finish it working together?

Solution:

With the above-mentioned chocolate method, you can solve this in the following steps.

• Assume work as chocolates
• Hence, the total no of chocolates to be consumed =18 units (LCM of 9 and 18)
• This means X can eat 18 chocolates in 9 days.
• X consumes chocolates in one day = 2 units.
• Y can eat 18 chocolates in 18 days.
• Y consumes chocolates in one day = 1 unit per day
• Chocolates consumed by X and Y in one day together = 3 units
• Time taken by both of them to consume 18 chocolates = 18/3 = 6 days

#### 2nd Approach: Per Day’s Work

In the event that X can finish the work in ‘a’ days and Y can finish a similar work in ‘b’ days, when they cooperate, the time taken to finish the work is given as following.

X can finish the work in ‘a’ days. So in one day, he will do 1/a of the work. Y can finish the work in ‘b’ days. So in one day, he will do 1/b of the work. Complete work done by both in one day = (1/a) + (1/b). Thus, the total time needed to fulfill the work = (ab)/(a +b) days.

Question: If X finishes the entire work in 10 days, Y finishes the work in 12 days. In how many days can X, Y day finish the work when worked together?

Solution: 60/11 days

• Since X finishes the entire work in 10 days, X completes 1/10th of the work in 1 day.
• Since Y finishes the entire work in 12 days, Y completes 1/12th of the work in 1 day.
• Working together they can finish the work =1/10+1/12 = 11/60 of the work in 1 day. Hence total days taken by both of them to finish the work = 60/11 days.

#### 3rd Approach: LCM Method

In this method, we expect the total sum of work to be finished as a finite divisible and dependent on it, we continue with the calculation. To make the calculation easier, suppose the total sum of work to be finished as the LCM of time taken by various people to finish a similar work.

In the event that X can finish the work in ‘a’ days and Y can finish a similar work in ‘b’ days when they cooperate, the time taken to finish the work is given as following.

Question: If X finishes the entire work in 10 days, Y finishes the work in 12 days. In how many days can X, Y day finish the work when worked together?

Solution:

Let the amount of piece of work be 60 units (LCM of 10 and 12). Since X works 60 units in 10 days, so he works 6 units every day. Since Y works 60 units in 12 days, he works 5 units every day. Working together, they do 6 + 5 = 11 units each day. Hence to complete 60 units of work, both together will take 60/11 days.

### Work Equivalence

In the man-days concept questions, we assume that all men work with the same efficiency unless it is given in the question. The relationship between the number of people working(N), the total number of hours worked per day(H), the total number of days worked(D) and quantity of work done(W) for different cases is as follows:

N(1) x D(1) x H(1)/W(1) = N(2) x D(2) x H(2)/W(2)

For the above equations, the relationship between variables is as follows:

• The total number of people working and work done are directly proportional
• The amount of work done and the number of days worked is directly proportional
• The total number of people working and the number of days worked is inversely proportional.

We hope that now you got the complete idea of Time and Work. Follow all the strategies and tricks mentioned above to improve your problem-solving skills. If you need any further clarification, you can ask us through the contact us page or in the comment box mentioned below. Bookmark our site to get all instant and latest updates.

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