Time and Work Part 1 -Aptitude in English
Time and Work
Time and work are important concepts that are related to our daily lives. Time is
precious and work is worship, so we have a lot to do with time. Let's learn about
the different models and varieties of how to think about time and work.
Here is a simple way to approach questions involving time and work:
• For questions where two people are involved and no conditions are given,
the answer is the product of two numbers divided by the sum of two
numbers.
• Example: A and B can do a job in 20 and 30 days respectively. Find the time
taken if they work together.
Solution: Answer for A and B is equal to the product of 20 and 30 divided
by the sum of 20 and 30. So, the answer is 12 days.
• If both A and B are given independently and together they can complete
the work, then the answer is the product of two numbers divided by the
sum of two numbers.
• Example: A can do a job in 40 days and B can do it in 30 days. Find the time
taken if they work together.
Solution: Answer for A and B is equal to the product of 40 and 30 divided
by the sum of 40 and 30. So, the answer is 13 1/3 days.
• If a person leaves the work in between, then use the product by difference
method.
• Example: A can do a job in 40 days and B can do it in 60 days. Find the time
taken if they work together, but A leaves the work after 20 days.
Solution: Answer is equal to the product of 40 and 60 divided by 60 minus
40, which is 120 minutes or 2 hours.
• For questions involving multiple conditions and people leaving or joining in
between, a more complex approach is required.
• It is important to note that the above methods only work for questions
involving two people and no conditions.
Work Completion Question
, Given three workers A, B, and C started working and suddenly A left and then B left.
How long will it take for C to complete the remaining work?
To answer this question, we need to find the LCM of the time required for each
worker to complete the work. Let's denote the time required for A, B, and C as a, b,
and c respectively. Then, we can express the work rate of each worker as:
• A's work rate = 1/a
• B's work rate = 1/b
• C's work rate = 1/c
To find the LCM of a, b, and c, we can follow these steps:
1. Find the prime factors of each number
2. Multiply the highest powers of all the factors to get the LCM
Once we have the LCM, we can find the work rate of each worker and add them up
to get the work rate of all three workers. Then, we can use the work formula, work
= rate * time, to find the time required for C to complete the remaining work.
It is important to ensure that the workers are not fighting among themselves and
working together towards completing the work. The total work required should be
divided into equal parts and assigned to each worker based on their work rate.
Let's assume the total work required is 120 parts. Then, we can find the work rate of
each worker as:
• A's work rate = 1/20 = 6/120
• B's work rate = 1/30 = 4/120
• C's work rate = 1/40 = 3/120
If all three workers work together without any disturbance, they can complete 13
parts of work every day. If A worked for 5 days before leaving, then 65 parts of
work would have been completed. To find the remaining work, we can subtract 65
from 120, which gives us 55 parts of work. Now, we can use the work formula to
find the time required for C to complete the remaining work:
Work = Rate * Time
55 = (3/120) * Time
Time = 220 days
Time and Work
Time and work are important concepts that are related to our daily lives. Time is
precious and work is worship, so we have a lot to do with time. Let's learn about
the different models and varieties of how to think about time and work.
Here is a simple way to approach questions involving time and work:
• For questions where two people are involved and no conditions are given,
the answer is the product of two numbers divided by the sum of two
numbers.
• Example: A and B can do a job in 20 and 30 days respectively. Find the time
taken if they work together.
Solution: Answer for A and B is equal to the product of 20 and 30 divided
by the sum of 20 and 30. So, the answer is 12 days.
• If both A and B are given independently and together they can complete
the work, then the answer is the product of two numbers divided by the
sum of two numbers.
• Example: A can do a job in 40 days and B can do it in 30 days. Find the time
taken if they work together.
Solution: Answer for A and B is equal to the product of 40 and 30 divided
by the sum of 40 and 30. So, the answer is 13 1/3 days.
• If a person leaves the work in between, then use the product by difference
method.
• Example: A can do a job in 40 days and B can do it in 60 days. Find the time
taken if they work together, but A leaves the work after 20 days.
Solution: Answer is equal to the product of 40 and 60 divided by 60 minus
40, which is 120 minutes or 2 hours.
• For questions involving multiple conditions and people leaving or joining in
between, a more complex approach is required.
• It is important to note that the above methods only work for questions
involving two people and no conditions.
Work Completion Question
, Given three workers A, B, and C started working and suddenly A left and then B left.
How long will it take for C to complete the remaining work?
To answer this question, we need to find the LCM of the time required for each
worker to complete the work. Let's denote the time required for A, B, and C as a, b,
and c respectively. Then, we can express the work rate of each worker as:
• A's work rate = 1/a
• B's work rate = 1/b
• C's work rate = 1/c
To find the LCM of a, b, and c, we can follow these steps:
1. Find the prime factors of each number
2. Multiply the highest powers of all the factors to get the LCM
Once we have the LCM, we can find the work rate of each worker and add them up
to get the work rate of all three workers. Then, we can use the work formula, work
= rate * time, to find the time required for C to complete the remaining work.
It is important to ensure that the workers are not fighting among themselves and
working together towards completing the work. The total work required should be
divided into equal parts and assigned to each worker based on their work rate.
Let's assume the total work required is 120 parts. Then, we can find the work rate of
each worker as:
• A's work rate = 1/20 = 6/120
• B's work rate = 1/30 = 4/120
• C's work rate = 1/40 = 3/120
If all three workers work together without any disturbance, they can complete 13
parts of work every day. If A worked for 5 days before leaving, then 65 parts of
work would have been completed. To find the remaining work, we can subtract 65
from 120, which gives us 55 parts of work. Now, we can use the work formula to
find the time required for C to complete the remaining work:
Work = Rate * Time
55 = (3/120) * Time
Time = 220 days
