# Time and Work Questions

Are you trying to ace the GMAT? Time and work questions are very relevant and an important aspect of the quantitative section of the examination. They are easy-to-do quick numericals and with the right amount of practice and knowledge, you can easily complete them efficiently without wasting a majority part of your exam time. Here is all the information that you will need about the time and work questions and how to go about them.

## Time and Work Questions: Concepts

There are certain concepts that are fundamental to the understanding of these questions, once these basic concepts are clear to you, solving the questions will be extremely easy. Here is a brief analysis of the concepts relevant to the time and work questions:

• Time X Rate of Work  = Total Work Done

T X R = W

• Time and work are inversely related. That means that the more amount of time it takes to do a job, the less amount of work is completed.
• Rate of work and time are also inversely related. This is to say, the higher the rate of doing work, lesser the amount of time it takes to complete the work.

Let us try to understand these concepts with the help of an example:

If G takes 7 days to complete a piece of work alone, then in 1 day he completes 1/7th portion of the work.

If K takes 6 days to complete a piece of work alone, then in 1 day he completes 1/6th portion of the work.

Thus, in 1 day, they together complete 1/7th + 1/6th of the work.

## Time and Work Questions Tricks

The LCM Trick is one of the easiest ways of mastering the time and work questions, understanding this trick will ensure that you solve the questions efficiently and accurately. Here is the LCM trick explained with the help of examples so that you get a better understanding of how to go about it:

Example 1 of Time and Work Questions

Suppose G completes work in 15 days and K completes the same work in 10 days by themselves. In what number of days will they complete the work together?

Solution: Take the LCM of both the numbers which denotes the time taken by each individual to complete the work.

So, LCM of 15 and 10 = 30

Since G takes 6 days to complete the work. In one day he will manage 30/15 = 2 units.

Following a similar logic, K takes 10 days to complete the work and so in one day, K does 30/10 = 3 units of work.

Together in a day, they complete 2 + 3 = 5 units of work.

To further calculate how much time they will need to complete the work together:

30 (total work) / 5 (combined work in 1 day) = 6 days.

Hence, they require 6 days to complete the work together.

Example 2 of Time and Work Questions

It takes 15 days for G to complete the work alone while K takes 10 days to complete the same work alone. They start working but K leaves after 2 days and goes away. In what time will G complete the remaining work?

Solution: Taking the LCM as described above; LCM = 30.

Since G takes 6 days to complete the work. In one day he will manage 30/15 = 2 units.

Following a similar logic, K takes 10 days to complete the work and so in one day K does 30/10 = 3 units of work.

G does 2 units in a day and K does 3 units in a day. They worked together for the first two days and so work done in the first two days = 5X2 = 10 units.

Out of the total work, units left are 30-10 = 20 units.

These 20 units need to be completed by G alone. Time required by G to finish this work = 20/2 = 10 days.

Thus, G will take another 10 days to complete the remaining work.

Example 3 of Time and Work Questions

G starts to make a painting at the rate of work of 3 units in a day while K spoils the painting made by G at the rate of 2 units per day. How many days will it take to complete the painting which comprises of let us say 10 units of work?

Solution: G paints, thus work done is +3 units per day while K spoils the painting and hence work done is -2 units per day. Net work done in a day = +3-2 = 1 unit per day.

Watch this video to learn some quick tricks to solve time and work questions-

## List of Time and Work Questions

Here are some important questions to practice-

12 Men or 18 women can reap a field in 14 days. The number of days that 8 men and 16 women will take to reap it?

A. 7 days
B. 8 days
C. 9 days
D. 10 days

A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

A) 1/24 day

B) 7/24 day

C) 3(3/7) days

D) 4 days

Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

A) 7

B) 8

C) 12

D) Cannot be determined

A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.

• A. 2 days
• B. 1 ½ days
• C. 3 days
• D. 3 ½ days

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

1. 12 days
2. 15 days
3. 18 days
4. 16 days

A and B can do a piece of work in 4 days, while C and D can do the same work in 12 days. In how many days will A, B, C and D do it together?

1. 12 days

2. 4 days

3. 3 days

4. 2 days

A, B, and C can do a piece of work in 8 days. B and C together do it in 24 days. B alone can do it in 40 days. In what time will it be done by C working alone?

1. 25 days

2. 24 days

3. 60 days

4. 20 days

5. 30 days

Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?

A. Rs. 50

B. Rs. 60

C. Rs. 70

D. Rs. 80