Hello everyone, welcome back to our new video.
Today's topic will be related to time and work.
We have done the topic of time and speed and distance.
Now the next topic is related to time and work.
There is no formula for time and work.
You have to learn it from your daily life.
You have to learn and build relations.
If we look at time and work, work means whatever work we
are doing, whatever work we have done, it can be work.
X, Y, Z, anything can be work.
And time is how many days, days, hours we are working.
That will come in our time.
So time, how much work we have done, suppose we have done
it in 10 days.
If we increase that same work, suppose we had to read 10
books in 10 days.
Now if we have to read 20 books, then obviously the number
of days we will take to read those 20 books, will also
increase. So as we have more work, the number of days to do
it will also increase.
So what do we know from this? We know that the relation
between time and work is directly proportional.
I had told you the definition of directly proportional.
So it is related to that.
If our work increases, it means we will take more time to
do that work as compared to less work. So this is the
relation we will have.
That time, how much time we will take, if we are taking
more time, which means we have more work, then what is the
relation between time and work?
It is directly proportional.
If time is more, then work will be more.
If work is more, then time is more.
Now what do we see?
The main thing we focus on, is how much work is being done
in a day.
We focus more on that.
And with the help of that, we solve the questions.
So we have to focus on how much work is being done in a day.
Suppose I tell you, that there is a person, Raj.
He can do any particular work,
He can do any particular work.
How many days does it take him to do that work?
It takes him 10 days to do one particular work.
So first of all, what we will do in these cases, we will
find out the work done in a day.
How much work is being done in a day?
We will find out his one day work.
So if he is doing total work in 10 days, what is the
indirect meaning of this? Raj is taking 10 days to complete
a particular work.
That work can be anything.
He is taking 10 days.
So how much work will he do in one day?
When he will do the whole work in 10 days, then what will
we take for the whole work?
Like in percentage, in probability, you will see later,
what we used to take in percentage? We used to have the
whole percentage, 100%.
Similarly, in probability, the maximum probability we had
was 1. Similarly, in work, if we see the whole work, like
we used to see in fractions, that if we see a whole thing,
then we used to do its fraction.
But what was the whole?
It was only 1.
Similarly, what are we taking for the work? We take the
whole work.
Let us suppose that this is 1 unit.
This is 1.
We are taking this as 1.
So if this 1 unit is doing the work in 10 days, then how
much work will he do in one day?
Work done in one day.
That will always be whatever time we have.
Right now, we have 10 days.
In 10 days, he is doing the whole work.
So in one day, how much work will he do every day? 1 by 10.
Obviously, Obviously, he must be doing 1 by 10 work in one
day.
That is why he is doing 1 by 10, 1 by 10.
He must have done 1 by 10 work every day.
So what will he become in 10 days? The whole work will be
completed.
I hope this will be clear to you.
If he is doing 1 by 10 work in one day, means he is doing 1
portion out of 10.
So how much time will it take him to do 10 portions?
Obviously, it will take 10 days.
How much time will it take him to do 10 portions, when he
is doing 1 by 10 work in one day?
So what will we get out of this? If we are given that he is
doing 1 work in 10 days, then what will we get out of these
questions?
We will get out how much work he is doing in one day.
Work done in one day.
And whatever work he is doing in one day, we call it
efficiency.
Efficiency.
Efficiency means how efficiently he is working.
How fast or how fast, in layman terms, how efficiently he
is working.
Suppose Raj did this work in 10 days.
But some other person,
He is doing this work in 8 days.
The same work which Raj did, the same work X is doing in 8
days.
So what will you get out of this?
What will we get out of this?
That Raj is taking more time, means he is slow in work.
And X is taking less time.
He is completing this work in 8 days.
So this tells us his speed, how efficiently he is working.
So this tells us his efficiency.
This is called his efficiency.
So Raj's efficiency, means how much work he did in one day.
That will be 1 by 10.
Similarly, if we take out X's efficiency, means work done
by X in one day.
What will that be? 1 by 8.
You don't have to do anything.
You have to divide all the days into 1 by number of days.
What will you get?
You will get efficiency and work done in one day.
So this is where your formula comes from.
Which will be your formula.
And you will also use time.
Time means how many days are taking us to do that work.
Similarly, if we do into efficiency, say efficiency, or in
one day, you can write it in brackets, work done in one day.
How much work is being done in one day.
Whatever work is being done in one day, if we multiply it
by the total number of days, what will we get?
We will get total work.
Because that is the whole work.
Total work will be obtained.
So this becomes your general formula of time and work.
This will also help you understand the relation.
Who is proportional to whom.
Now see, I told you that time and work are proportional to
each other.
So see, both are coming in front of each other.
So it is proportional.
Similarly, if I tell you that time, time, keep time aside,
and make it equal to total work upon efficiency.
So what will we get?
Total work upon efficiency will give us time.
Which means total number of days.
What is time?
Total number of days or hours.
So total number of days will be our time.
So see this relation.
What is the relation between time and efficiency?
If we keep work constant, as we learned in ratio and
proportion, if we keep one thing constant, if we keep work
constant, what is time?
We have time.
If it is constant, what is work?
Write efficiency below.
So are they inversely proportional to each other?
No.
Time is inversely proportional to efficiency.
If I explain it to you in normal language, the more
efficiently we work, means the more speed we work,
obviously it will take less time for us to work.
is a Suppose we do any question that there is a person who
has done a work and he is taking time to do that work.
He thinks that he can do a work in n days.
He thinks that he is taking n days to do any particular
work.
So first of all we will write A's one day work.
A's one day work.
Means how much work does A do in one day.
Or you can write work done by A in one day.
What name were we giving to this? We were also calling this
efficiency.
So how much will A's one day work be?
Total work, we are taking 1 now.
So 1, because we are not given anything.
Divide it by how many days we are taking to do that work.
Divide it by that.
So what will you get?
A's one day work will be 1 upon n.
Means how many days are taking, divide that by 1.
So what is this?
Work done by A in one day.
Or efficiency of A.
Now if I ask the opposite of the same thing.
If I ask the back case of this.
That A's efficiency is 1 by n.
Means in one day he is doing 1 by n work.
So how many days will it take him to do that work.
So what we will do in this? In this we will make it
opposite.
We will make it reciprocal again.
If we were given this.
This was given to us.
And we took it out in our way.
But next case is case 2.
If we see case 2.
We are given this.
Now what is given to us?
A's one day work is given to us.
That is he is doing 1 by n work in one day.
So how many days will it take him to complete this task.
So total time or number of days taken by A.
To complete the work.
The given work.
Whatever work is given to us.
Given work would be.
We don't have to do anything.
Just make it opposite or reciprocal.
So what will be the reciprocal of 1 by n?
So it will take him n days to complete this task.
So you should know this relation.
If we are given one day efficiency.
Then make it reciprocal.
You will get time.
And if you are given time or days.
Then make it reciprocal.
What will you get?
You will get efficiency.
Or whatever work is done in one day.
You will get that.
Have you understood this much?
The next thing related to this.
If you are given.
I hope it will be clear.
How to get work from days.
And how to get days from work.
So we don't have to do anything.
We just have to make it reciprocal.
Nothing else.
Now we have two persons.
Till now we were doing for one person.
One by A.
And we were taking out the data for that.
We were taking out the efficiency.
How many days it takes.
How much work is done in how many days.
How efficiently it is done.
Now we have two persons.
One is A.
One is B.
Suppose A is taking some days.
A is taking x days to complete a certain work.
And B is taking y days to complete that same work.
It means.
There is a work.
A is told to do.
And B is also told to do.
Suppose A is told.
To clean the whole city.
So A is taking x days to do that work.
And B is taking y days to do the same work.
Now if we see.
Both are doing their work in their own way.
But.
If we tell them.
Instead of doing it separately.
If you both do the work together.
Then your work will get done faster.
Isn't it?
It is possible.
If two persons do the work together.
Except the group studies.
Which you do.
Then your work will get done faster.
So what we have to find out.
A and B.
If they work together.
Work together.
Then how many days will it take them.
To complete the given task.
So both of them.
How many days will it take them.
To complete the given task.
How will we find this out?
Simply.
What should you do?
First of all.
Think about it.
Suppose A is taking.
5 days to do a work.
And B is taking 7 days.
To do that work.
So how will you find out.
If A and B.
If they work together.
Then how many days will it take them.
So what will we find out.
First we will find out.
Efficiency.
Means one day's work.
What will be the work of one day.
So if A is completing the work.
In X days.
Or 5 days.
Then what will be the work of A.
If he is working in 5 days.
Then how much work will he be doing in one day.
1 by 5.
Work done in.
One day.
What will be the work of A.
So what will happen.
Whatever time is given.
Reciprocate it.
So that will be 1 by 5.
So this is efficiency of A.
Efficiency of A.
Or work done by A.
In one day.
That is 1 by 5.
Similarly we will find out the work of B.
So what will be the efficiency of B.
1 by 7.
Because it will take 7 days.
Now if we have to combine both.
In one day.
A is able to do this much work.
And in one day B is able to do this much work.
So how much work will both of them be able to do.
In one day.
If we add up the speed of both.
Then we will get the work of both.
How much work did both of them do in one day.
So what will we do.
A and B.
Both of them work.
In one day.
Work.
In one day.
Means how much work are both of them doing in one day.
How much work will they do.
How much work did A do individually.
If we add up the work of both.
Then we will get the work of both.
1 by 5 plus 1 by 7.
If we solve this.
Then what will be the efficiency of both of them.
Means the combined efficiency of both of them.
How much is the efficiency of both of them.
In one day.
Means how much work did both of them do in one day.
Together.
If we solve this.
We will get the work of both.
And we will get the work of both.
We will get the work of both.
12 by 35.
What is 12 by 35.
The efficiency of both of them.
Means how much work did both of them do in one day.
How much work did both of them do in one day.
Together.
So how much work will they do in one day.
When we have the work of one day.
Then what did I say for one day.
If we reciprocate that.
Then the total work that they will do.
Total time that they will do.
How much work will they do.
So the reciprocal of this.
That is 35 by 12 days.
If you cancel out that.
In days.
Then that will happen.
Similarly we have to do here.
When we are given x days a.
And y days b.
Then what will be the efficiency of a.
Tell me quickly.
Efficiency of a will be.
1 by a.
Efficiency of a.
This will be 1 by x.
this one day.
That would be a?s efficiency 1 by x plus 1 by y.
That would be x, y and x plus
So this is your direct formula, it is not necessary that
you remember this and do it.
You just keep in mind that what we have to do is to add up
the individual efficiency of both of them to get the
combined efficiency.
So we added up.
Now as soon as we add up and get the answer, it is
efficiency of A and B.
So how many days will be there? Days will be there.
Days complete the task.
And who is completing the task? Days taken by A and B.
How many days will they take together? They will take,
their reciprocal will be XY upon X plus Y days.
We will get so many days to do so many tasks.
Similarly, if we have an example of 2, how can we carry it
forward? We can do it in the example of 3.
How can we do it in the example of 3?
Now we will have 3 people, A, B, C.
Will they take X days?
They will take Y days.
And C is taking Z days to complete a work.
So we will get the efficiency of all of them.
Efficiency of A will be 1 by X, Efficiency of B will be 1
by Y,
And efficiency of C will be 1 by Z.
So together, if we are asked that how fast can A, B, C work
together?
So how will they do it?
First, we will get the combined efficiency of all of them.
How will the combined efficiency of all of them come out?
Add up the efficiency of all of them individually.
So we will add up 1 by X, plus 1 by Y, plus 1 by Z.
We will add it up.
Its LCM will be XYZ.
And if we solve it, we have to make XYZ above X.
So it will be YZ.
Here Y is there, we have to make XZ.
So it is XZ plus Z.
We also need X and Y.
So we will have to multiply it by XY.
So this is our efficiency.
Now if I ask for time,
So time will be reciprocal.
That is XYZ will come up.
And it will be YZ plus XZ plus XY.
See this cycle is going on.
First X with Y, then Y with Z, Then Z with X.
This is the cycle XYZ.
So first X with Y, then Y with Z, Then Z with X.
So these three pairs are formed here.
After taking LCM.
So it will be so clear to you.
So let's do related questions.
Then it will be more clear.
Till we don't do questions, we don't know.
See the question.
Read the question.
A can do a work in 6 days.
A is a person.
How many days is he working?
He is taking 6 days.
So how much time is A taking? 6 days.
Similarly B is doing it in 9 days.
B is taking 9 days.
In how many days will both complete the work together?
We are asked that how many days will both work together?
This is a case of work together.
So how many days will both work together?
First of all, we will find out their individual efficiency.
So efficiency of A.
What will be the efficiency of A?
If I denote the efficiency of A with EA,
It will be 1 upon
Whatever days he is taking,
So efficiency of A would be 1 by 6.
And what else can we call it?
Work done by A in one day.
Or A's one day work.
Similarly, we will find out the efficiency of B.
Or B's one day work.
That would be 1 by 9.
Now if we find out the efficiency of both,
Then what will be the combined efficiency of both?
That is, A plus B's one day work.
A, B and B's one day work.
How much will it be? 1 upon 6 plus 1 by 9. Now we need time.
So solving this and finding out its reciprocal, We will get
the number of days.
So solve it.
Either you take the LCM or multiply both.
6 into 9.
And here 6 and 9 are required.
So 9 plus 6.
Solve it.
So what will it be? 15 by 6 into 9.
So this is being cancelled by 3.
So 3 times 2 is 3 times 5.
So this is 5 by 18.
So this is the combined efficiency of A and B.
So time.
What will be the number of days? 18 by 5. Number of days.
Complete the task together.
Means how many days will come to complete the task together?
That would be 18 by 5.
What should I do for efficiency?
Reciprocate it.
You will get the number of days.
So 18 by 5.
If we see it like this,
We will have to tell the number of days.
So 15 by 3.
Then 30.
So this is 3.6 days.
How many days will it take us to complete this task?
It will take us 3.6 days to complete the work.
When? When both of them will work together. When both of
them will work together, It will take us so much time.
It was easier than the question.
See next.
And this is a new category along with the question.
But don't take it as a new category.
This type of question.
Understand the type of question.
You can use the same category or formula.
So read the question.
What is the question saying?
There are two persons.
X and Y together can do a work in 10 days.
X and Y are working together.
So how much time will it take them? 10 days.
So X and Y.
When they are working together,
It will take them 10 days.
X alone can do it in 30 days.
If X is doing the same work alone.
If X is doing it alone,
It will take him 30 days.
So we were asked,
The time in which Y alone can do the work.
So this is your type.
This is your new type of question.
That is,
In how many days Y alone can do the work?
So we have to find out,
In how many days Y alone can do the work?
So what is this same?
This same is related to our last question.
We will follow the same steps.
You had to see,
What was in the last question?
The combination of A and B,
Whose was it equal to?
Equal to the individual efficiency of both.
So put the same formula here.
The efficiency of X and Y combined,
It should be equal to their individual efficiency.
So we have to find out the individual of X.
So let's do it.
X The work done by Y,
Is equal to the work done by X. Let us suppose that Y alone
is completing the work in X days.
Now, what we will get next? We will get efficiency.
So, what will be the efficiency of X plus Y together? 1 by
10.
What will be the efficiency of X? 1 by 30. So, we have
taken efficiency of X as 1 by 30.
Now, we will find the efficiency of Y.
What have we done to Y?
We have let X.
It is taking X number of days.
What have we done to it?
We have let it.
So, what will be the efficiency of it? 1 by X. Now, what we
have to do?
We had seen in the last question also.
The combined efficiency of A and B was equal to the
individual efficiency.
Similarly, in this question also, the combined efficiency
of X and Y will be equal to the individual efficiency.
So, the efficiency of X plus Y should be equal to the
efficiency of X plus efficiency of Y.
Now, there is one unknown in this.
Keep the value of X aside.
Take the other things aside and solve it.
So, 1 by 10 minus 1 by 30 would be equal to 1 by X.
If we take LCM, it will be 30.
3 minus 1.
1 by X.
So, what is the value of 1 by X? 2 by 15. 2 by 30, that is
1 by 15.
So, this is the value of 1 by X.
So, the efficiency of Y has come.
But, we have to find out the days of it.
So, the reciprocal of efficiency will be days.
So, we had to find out the value of X.
So, we will reciprocalize X.
We need the value of X.
So, what will be the value of X? 15 days.
So, the answer of this will be 15 days.
If Y does this work alone, then how many days will it
complete?
It will complete in 15 days.
So, it is not necessary that you have to remember the new
formula.
If you have to remember the new formula, then what will it
become? It will become X minus Y divided by XY.
What will be the value of Y? One will be of together.
What will be the value of together? What is the work of
together?
This one, Y.
That means, the efficiency of the work done by both of them
together.
So, if you get confused in the formula, then it is not
necessary.
You can solve it with the help of the last formula.
So, I hope that you have understood the introduction in
today's class.
And, you must have understood these two types of questions.
In the next class, we will discuss the types and cases of
these questions.
Till then, keep practicing.
And, thank you for watching the video.
If you refer the certificate course in HR and Admin to your
friends, and they sign up using your referral code, you'll
get some awesome rewards.
That sounds interesting.
For every friend you refer, you earn points that you can
redeem for discounts or even cash rewards.
Count me in. I'll make sure to spread the word to all my
friends.