Hello everyone, welcome back to a new video.
In the last video, what we did in yesterday's video, we saw
the introduction of work and time, and based on that, we
did 1-2 questions.
Today, we will continue from there.
I hope you remember the formulas I made you do yesterday,
the formulas I made you write, the concept I taught you,
related to work and time, and related to efficiency, you
will remember all that.
So, we will proceed on that basis.
So, remember and recall what we did yesterday.
The main formula for work and time, what did we do?
Time into efficiency, time into efficiency, is equal to
work done.
This is what we wrote, and in another way, what did we
write?
Time is equal to time taken, means how will total time
taken come out?
Is equal to total work done, divided by efficiency.
Means, work done in one day.
Means, the work done in one day, what did we call it? We
called it efficiency.
This is what we learnt.
Then we saw, what is the relation of time with work?
So, we said that time is directly proportional to work.
Similarly, we saw the relation of time and efficiency, that
time is inversely proportional to efficiency.
What is efficiency?
Efficiency is how much a person is able to work in one day.
What is his capacity to work in one day?
That is what is called efficiency.
So, total time into efficiency, is equal to total work done.
Then we asked a question, that if we have two people, A and
B, and we have given individual time for both of them, that
one worked in one day, and one worked in one day.
So, how many days will they work together?
So, we saw the formula for that, that the sum of efficiency
of both of them, is equal to total efficiency of both of
them.
Similarly, we saw in case of three, that if A, B, C, then
if we have given individual efficiency of all three, then
what did we do?
We took out their total efficiency, and then reciprocated
it, that how much time will they take.
So, these types of questions, were of what type?
When we have given individual efficiency of all three, and
at last, we have to take out their total, that how much
time will it take for them to work together.
So, we had to take out efficiency of all three, when we
have given individual efficiency of all three.
Now, if we see a new case,
I will tell you a new case, and we will do a question based
on it.
So, we did this last, we did formula for three, and formula
for two.
And we did one more type of question, that if we have been
given combined efficiency of A and B, that how much time
they are working together, time is given, and if A works
alone for how many days, then how much time B will be able
to work alone.
This alone formula, we derived it from this.
We were just putting it in formula, and whatever value of B
we had to find out, we found out.
For that, we did not have to remember the new formula, we
did it in that.
So, the new case that we will do today, what type of new
case is yours?
It is of this type, like we have three people,
A, B and C.
These three people are there.
Now, these three people, the question till now was, that we
were given individual efficiency of three people, or how
much time they were taking individually, that was given.
Then we had to find out the total.
But now, what will be given?
We will be given efficiency in pairs of two.
How in pairs of two?
Like efficiency of A and B is given, that these two took so
much time, then B and C will be given, then C and A.
These three pairs will be formed.
So, what is given for these three pairs?
Efficiency is given, that if A and B work together, then
they will work with some efficiency.
B and C will work with some efficiency.
Let us suppose, efficiency of A and B is X.
We are writing this as efficiency.
Some efficiency of B and C is Y.
And some efficiency of C and A will be Z.
We are given this.
Then we are given, that if these three work together,
means, A, B and C.
We will have to repeat it twice.
A, B and C.
If these three work together, then how many days will their
work be over?
So, in this case, how will we solve the question?
Because in this case, individual efficiency is not given,
but it is given in pairs.
So, you see, how can we think about it?
How can it be?
In that also, if we have to find the total efficiency, then
we add the individual efficiency.
Now, individual efficiency is not given.
So, we add what is given.
So, A and B are given.
So, if I am adding efficiency, adding efficiency,
Right? What we are doing is, we are adding efficiency.
So, A and B are given.
A and B have X given.
Then, we will add B and C.
If we add B and C's efficiency, then it will become Y.
Plus, if we add C and A, the combined efficiency, then
these three things are given.
If we add them, then it will become X plus Y plus Z.
This side will become X plus Y plus Z.
That is, the addition of efficiency of these three pairs.
X plus Y plus Z.
Now, if you solve these three, then see, how many times we
have A?
A is twice.
Efficiency of A is twice.
Similarly, B is also twice.
Efficiency of B is also twice.
And similarly, C is also twice.
So, what we had earlier, after solving, only A plus B plus
C was formed.
When we had individual efficiency, in this question, we
don't have that.
In this case, what is this side forming?
What is this forming?
A is twice.
B is twice.
So, we have twice A, B and C.
Their efficiency is being formed.
So, X plus Y plus Z.
The sum of these three pairs, whose equal will we get?
Twice their efficiency.
Now, twice their efficiency will be obtained, but we have
to find its single.
Then what we will do?
We will divide it by 2.
Whatever answer we get for efficiency, we will divide it by
2.
So, this is done.
It is not necessary, that efficiency is given here.
Here, apart from efficiency, time can also be given.
If time is given, then you can subtract efficiency from
time.
How will you subtract efficiency from time?
You can divide it by 1.
If you do efficiency, then time will come.
So, there is no problem in that.
Time can also be given.
And efficiency can also be given.
You just have to understand this, that now, this side which
is being formed, that is twice of A plus B plus C.
Efficiency is being formed.
It means, it is being doubled.
So, whatever answer we get, we will divide it by 2.
Did you understand?
Let's do one more question.
Then, you will understand better, how to apply.
See this question.
Read this once.
Read the question.
What is the question saying?
P and Q can do a work in 8 days.
Two people P and Q, how many days are they working?
They are doing the work in 8 days.
Similarly, Q and R, whatever is given, they keep writing.
P and Q.
Their time is given.
So, I am writing time on top.
P and Q are taking 8 days.
Similarly, Q and R, how many days are they taking?
Can do the same work.
We are talking about same work.
They are doing in 12 days.
So, they are doing in 12 days.
P, Q and R, together can finish it in 6 days. If we talk
about all three,
P, Q and R, all three, how many days are they doing the
work? They are doing in 6 days.
Now see, when they were two, they took more time to do the
work. When all three came together, they took less time to
finish the work.
Because more people are there, obviously it will take less
time.
Now see, what we have to find out?
P and Q together will do it in.
Now we have two pairs.
PQ and QR.
Now we have to find out for P and R.
P and R. How many days will it take to complete the work?
We have been asked this question.
So, we have to find out how to find out.
First of all, what is given in this question?
Time is given.
And three pairs are given.
P, Q, R, P and Q.
QR and PR.
And this is the given of P, Q and R.
We have to find out P and R in how much time.
First of all, with the help of time, find out the
efficiency of these three things.
Now, we will find out the efficiency.
One upon time.
We have to find out P and R.
So, what do we let?
We let P and R finish the work in X days.
So, whatever we have to find out, we write it as X days.
Let P and R together complete the work in X days.
We have let X days.
Now, make a column of efficiency.
What will be the column of efficiency?
P and Q will be 1 by 8.
Because time is 8 days.
So, 1 by 8.
Q and R will be 1 by 12.
P and R will be 1 by X.
And P, Q and R will be 1 by 6.
1 by 6.
Now, add these three.
If we add these three,
P and Q.
Q's efficiency.
Plus Q and R's efficiency.
Plus P and R's efficiency.
Whose equal will we get? If we add all these, what will
happen? 1 by 8 of P and Q. Plus Q and R's 1 by 12.
Plus P and R's 1 by X.
Whose equal will this be?
If we see this,
P is coming twice.
So, twice P, Q and R's efficiency.
Whose equal will this be?
Twice of P, Q and R's efficiency.
This was the main point.
This will be twice.
As we saw in the last formula.
When we are adding these pairs, we are getting two.
P's efficiency is coming twice.
Q's efficiency is coming twice.
R's efficiency is coming twice.
So, this will be twice.
Now, P, Q and R's efficiency is already given.
That is 1 by 6.
So, what value should I put instead of that? 1 by 6.
So, solve this.
Leave 1 by X aside.
Take the remaining things to that side.
So, this will be 2 into P, Q and R's efficiency.
1 by 6.
Now, if we take 1 by 8 there, it will be minus 1 by 8.
If we take 12 plus 1 by 12, it will be minus 1 by 12.
Solve this.
So, this is 3 from 2.
Now, take the calcium of 3, 8 and 12.
What is coming? 3, 8 and 12.
3, 4.
Then, it is 8.
So, we will get the calcium of 3.
We will get the calcium of 3.
It is 24.
So, 24.
Now, if we make 3 into 24, we will have to divide 3 by 8.
So, 3 into 8 is 24.
So, 8 will come up.
If we make 8 into 24, 3 is 3. If we make 12 into 24, we
will have to divide 2 by 2.
It is minus 2.
So, what do we have?
Minus 3 minus 2 is minus 5.
So, 8 minus 5 would be 3.
So, we have 3 by 24.
That is 1 by 8.
So, what is the answer of 1 by 8? 1 by X. We wanted X.
1 by X is efficiency.
That is 1 by 8.
But, we need time X.
So, let us reciprocate.
What will be the value of X? 8.
If we want to see the time of P and R, that how many days
they can complete this task, together, both will be able to
complete the task in 8 days. The answer will be 8.
I hope it will be clear to you, what I have explained.
The main point here is that it becomes 2.
When the individual efficiency is given, then we will not
get 2.
But, when we have the pair wise efficiency, then we will
get 2.
Got it?
Now, let us move on to the next topic.
This was the case.
The next topic will be, if the ratio of efficiency of two
persons is given.
Efficiency.
If I am telling you that, one person is more efficient than
the other person, means that person is working faster than
the other person.
Means, he is working faster.
If he is working faster than the other person, then he will
take less time.
He will take less time than the other person, because his
speed is more.
He is more efficient than the other person.
So, he will take less time to do the same work.
Similarly, the other person will take more time.
So, if the ratio of efficiency is given.
Ratio in their efficiency.
Ratio of their efficiency.
If the ratio of efficiency is given.
What did I tell you about efficiency? Efficiency is work
done in one day.
Suppose, the ratio is given.
There are two persons.
One person is A and one person is B.
We have to divide their work done by A, ratio work done by
B in same time.
Ratio work done by B in equal time.
Equal time.
Efficiency means work done in one day.
But, if we take the ratio of equal time.
If there is a particular equal time.
For example, if there is one day, then one day.
If there is two days, then two days.
So, equal time.
We are counting the same time of both.
So, if the ratio of their work done is given.
That is efficiency.
In other words, if the ratio is given.
Let us suppose, the ratio is given.
X is equal to 1.
If we understand this in other words.
This is given to us.
That is, A is X times more efficient than B.
X is X times more efficient than B.
So, the ratio of their work done.
Work done by A, ratio work done by B.
If X is equal to 1.
So, A is working X times more efficiently than B.
In other words, X is working more efficiently than B.
Now, when they are working more efficiently.
In other words, they are working faster.
So, obviously, the time required to work will be less than
B.
Because, efficiency of B is less.
So, it will take more time than A.
So, if we have to find the ratio of time.
We are given the ratio of work done.
With the help of this, we have to find the ratio of time.
Time taken by A, ratio time taken by B.
So, what will be that?
That will be nothing.
That will be reciprocal.
In other words, it will be opposite.
If X is equal to 1, the ratio of efficiency or work done.
So, the ratio of time will be 1 is to X.
So, time taken.
Ratio of time taken by A and B.
First, we will write for A.
So, for A, it was X.
Now, for A, it will be 1 for time.
And for B, it will be X.
So, 1 is to X is the ratio of time.
So, the ratio of work done by A and B.
What will be that? x is to 1.
So this relation you remember.
On this basis we will see the question next.
So see the next question.
Read it.
The question says Anil is twice as good as Rahul.
Means he is two times as good as Rahul.
So this is giving us a comparison.
Means good is told that he is two times as good as Rahul.
Means indirectly his efficiency is told that his efficiency
is twice as good as Rahul.
And together they complete a piece of work in 20 days.
Together. If they work together then they complete the same
work in 20 days.
In how many days will Anil alone will finish the work.
If Anil works alone then in how many days he will complete
the task.
So let's see.
First write the given.
What is given?
If our efficiency of Anil.
Efficiency of Anil I will denote with EA.
EA Anil.
Efficiency of Anil is twice the efficiency of Rahul.
Twice the efficiency of Rahul.
Did everyone understand this? EA is equal to twice ER.
Because what is EA? Efficiency of A.
Efficiency of A.
And work done by A.
And what is ER? Efficiency of Rahul.
R is Rahul and A is for
Anil. And Rahul and work done by Rahul.
So this is efficiency.
Now if I take down ER then EA by ER.
How much is it? 2.
And we can write it as 2 by 1.
So if we convert it in ratio.
So efficiency of Anil.
Ratio efficiency of Rahul.
How much is it? 2 ratio 1.
See the question that we did in the last.
Should there be a ratio of efficiency? We got to know.
That is 2 is to 1.
So time ratio.
With the help of this, you just tell me the ratio of time.
What will be the ratio of time? Time ratio will be 1 is to
2.
Obviously, what will be the ratio of time? 1 is to 2.
Time of Anil.
Ratio time taken by Rahul would be 1 is to 2.
So the question is that both of them together take 20 days
to complete the work.
If we consider efficiency of Rahul as 2 and this is 1.
So what we have to do is to take out the days.
If they take 20 days, then how many days will Anil take
alone? So how will we do this question? Now if we get the
ratio of efficiency, then I have told you the ratio of time.
Now together they are completing the work in 20 days.
If they are completing the work together in 20 days, then
how much will be the efficiency of both of them together?
Means A and R.
will be the efficiency of Rahul and Anil together? How much
will be the efficiency of both of them together? It will be
reciprocal of time.
If they are taking 20 days, then efficiency of both of them
together will be 1 by 20.
Now apply the formula of efficiency.
Which formula?
If the efficiency of an individual is something, then its
sum should be equal to that of together.
So what we take? We have already taken that if the
efficiency of one is ea, then what will be the efficiency
of the other? If we take the efficiency of Rahul, then ea
will be 2er.
So we will put that.
Now put that efficiency of A plus efficiency of R, which
should be equal to the combined efficiency of both of them?
Efficiency of A plus R, means combined efficiency.
When they are working together, then how efficiently they
are working, then it should be equal to that.
So what will be the value of ea? We will put 2er.
So 2er
using this.
We have put the value of ea plus er is equal to, what is
its value? 1 by 20, 1 by 20.
Now we have only one unknown, that is er.
We will find out its value.
So these like terms will be added.
3er is equal to 1 by 20.
That is efficiency of Rahul, how much we got? We got 1 by
60.
That would be our efficiency of Rahul.
How much is Rahul's efficiency? 1 by 60.
If Rahul's efficiency is 1 by 60, then how much will be
Anil's efficiency? What will be ea? 2 into efficiency of
Rahul, that is 1 by 60.
So 2 into 60 cancels to 1 by 30.
So Anil's efficiency is 1 by 30.
When we got Anil's efficiency and Rahul's efficiency, then
we can also tell their time.
So how many days Rahul will take? 60 days because his
efficiency is 1 by 60 and Anil will take 20 days to
complete the same task because his efficiency is 1 by 30.
So we have to tell only Anil's efficiency.
So how much will be Rahul's answer? Time taken by Anil, how
much will be? Its reciprocal, that is 30 days.
So what will be its answer? 30 days.
I hope it is clear to you that if we have a ratio, then
with the help of ratio, how we have to move ahead.
Let's see next question.
What is the question? A is twice as good a workman as B.
Again the ratio is given that A is twice as efficient as B.
So if we take the ratio of A and B, whose? Their efficiency.
So what do we have? 2 into 1.
So what will be the time? 1 into 2.
And is therefore, if we do the time, then time A ratio B,
time taken by A.
I am writing in short, you can write in full.
If it is an objective question, then there is no need to
write in full.
Let's write in short.
So time ratio, time taken by A, ratio time taken by B, what
will be that? 1 into 2.
And is therefore, able to finish a piece of work in 30 days
less than B.
So what is the time taken by A? That A is able to finish
work 30 days earlier than B.
Because obviously he is more efficient than B.
So he will complete the work faster.
In how many days they can complete the whole work together?
So if they work together, then how many days will it take
them to complete the work? So this is the efficiency of the
individual.
If we take x of B, then what will be the efficiency of
A? 2x.
Similarly, we have taken the ratio of time.
So if we are given that both of them, what is the time
given? Suppose, let time taken by B to complete the task is
T days.
In T days, he is completing the work.
If B is taking T days, then time taken by A, what will be
the time taken by A? A is completing the work 30 days
earlier than B.
So if we subtract 30 from T, then we will get the time
taken by A, that A is taking so many days.
So T minus 30.
Now the ratio of time is already given.
So if we subtract the time of A ratio of B, then A is T
minus 30 and ratio of B is T.
So how much should we get? 1 ratio 2 and 1 by 2.
We understood that this is the ratio of time and the time
which we have taken individually, if we put their value,
then it will be 1 is to 2.
Now we have to find out the value of T, that is unknown.
So cross multiply it.
What will happen? 2T minus 2 into 30 that is 60 is equal to
T.
We will bring T here.
2T minus T is equal to 60 here.
So T is equal to 60.
So T is equal to 60 days because that is the time.
So B, whose time was T? B's.
How many days is B taking to complete? So B is taking 60
days.
So how many days will A take? 60 minus 30 days.
So time taken by A is equal to 30 days.
A is finishing 30 days.
In how many days they can complete the whole work together?
In how many days they can complete the whole work by
working together?
In how many days they can complete the whole work together?
In how many
days they can complete the whole work together?
In how many days they can complete the whole work together?
In how many
days they can complete the whole work together? In how many
days they can
complete the whole work together? In how many days they can
complete the
whole work together? In how many days they can complete the
whole work together? Now we will do a question based on
this.
Now we will do a question based on this.
So this was your work and time related questions.
We will see more deep level questions in next classes.
Thank you for watching.
Make sure to spread the word to all my friends.