### Problems on Time and Work are undoubtedly one of the most important set of questions when you are preparing for a competitive exam.

This is the 7

^{th}Smart Method in the series of blog posts that will help you solve questions in 5- 10 seconds that would otherwise take 30- 45 seconds.###
**What is Time and Work**

Time and Work involves dealing with rate at which individuals or group of people work. Conventionally we start by assuming the number of days (T) taken by the agent to complete a certain task where the rate of work of the agent is represented as 1/Tth part of the task.

Rate of work is the most important concept in problems on Time and Work because it makes it possible to sum up the effort of different agents working together where each of them has a different rate of work over a unit of time.

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**List of Formulas for Time and Work**

2. If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate of work), then

3. If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in

###
**Example of a Problem on Time and Work**

Sejal alone can complete a task in 12 days. She works alone for 4 days. She completes the remaining work in 4 days with the help of her colleague. How many days will the colleague alone take to complete the task?

1) 9 2)12 3)10 4) Cannot be determined 5) None of these

###

**Conventional Method to Solve Problems on Time and Work**

Assuming the rate of work of Sejal and her colleague, as S and C respectively, we get the following work equation-

**Step 1:**

W= Sx 12= Sx 4 + (S+C)x 4

**Step 2:**

12S= 4S+ 4S+ 4C

**Step 3:**

12S= 8S+ 4C

**Step 4:**

4S= 4C

**Step 5:**

S= C

The rate of work of Sejal and her colleague is the same which implies that both Sejal and her colleague take the same amount of time to do the same task.

Correct answer but problems on time and work when solved in the conventional way, require the framing of a very complicated equation and then solving it too… that is at least 30 seconds of work!

###

**Smart Method to Solve Problems on Time and Work**

Now here is the smart method that will save you at least 15 seconds!

Sejal works for 4 days alone and for 4 days with her colleague, which means that Sejal works for a total of 8 days. From this we know that Sejal has actually completed 8/12= (2/3) of the work, since 12 days is the total amount of time taken by her to complete the work.

*Assuming the total amount of work to be 1, we know that the remaining work is done by her colleague*

**Step 1:**

1- (2/3)= 1/3

We now know that her colleague did 1/3 of the work and worked for 4 days, which implies that her colleague can complete the total amount of work in

**Step 2:**

4x3= 12days

Isn’t it amazing how we have reached the answer in quick 10 seconds and just two steps!

Click on the video below to see our expert faculty explain this smart method.

Try this smart method right away by solving the above method to solve these questions-

**Question 1:**Ram alone can complete a task in 15 days. He works alone for 5 days. He completes the remaining work in 6 days with the help of his colleague. How many days will the colleague alone take to complete the task?

1) 22.5

**2)12 3)16 4) Cannot be determined 5) None of these****Question 2:**Nitin alone can complete a task in 20 days. He works alone for 5 days. He completes the remaining work in 5 days with the help of his colleague. How many days will the colleague alone take to complete the task?

1) 12 2)10

**3)15 4) 20 5) None of these**
Do leave your answers in the comments below.

Keep watching this space for more smart methods and till then keep practicing!

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