Hello everyone, welcome back to a new video.
The topic we are going to cover in today's video is not a
topic.
It has a lot of questions, but as if it has no theory.
The things we have learnt in Maths, like Ratio, Average,
Simple Calculation, Equation, we use those in this type of
questions.
So, today's topic is Problems on Age.
In every competitive exam, we see 1 or 2 questions on age.
And those are not based on any extreme or age formula.
They are just based on our basic Maths.
So, today we will see how to solve those problems, how to
tackle them, and practice questions on age.
So, for this, you should know about Average, Ratio and
Proportion.
And you should know how to solve Equations.
So, in this, you are given word problems.
For example, in the age of 2 random persons, there will be
a relation.
So, there will be a relation of few years back or few years
ahead.
And there will be a relation of present age also.
So, what we will do is, with the help of this data, we will
find out the age of those persons, if we ask present, then
present, and if we ask few years back, then few years back.
So, let's see how to solve these questions.
Then, accordingly, you will know how to solve age questions.
And this is a very easy topic.
If you watch even one video of this, you will know all the
questions.
Because, as such, this is not a difficult topic.
So, let's move on to the first question.
Age of Aman, the main trick to solve this is, to read the
word problems properly and formulate them.
That's all.
If you make a small mistake in reading the question, then
the calculation of the question will go wrong.
And your answer will be wrong.
So, let's read the first question.
What do you think is the meaning of the first line?
The first line tells us,
Aman, there are two persons, obviously Aman, and the second
one is Rahul.
The first line tells us about their age.
It doesn't tell us about their present.
It tells us about their age, 6 years from today.
6 years from today means 6 years afterwards.
It tells us about their future.
After 6 years, Aman will be 4 times the age of Rahul.
So, if the age of Aman is 7 times the age of Rahul, what is
the present age of Aman?
The relation given in the first line, is the relation given
6 years afterwards.
The relation given in the second line, is the relation
given in the age of Aman and Rahul.
But the relation given in the first line, is the relation
given in the age of Aman and Rahul.
The relation given in the second line, is the relation
given in the age of Aman and Rahul.
So, what is the present age of Aman?
We need to find the present age of Aman.
If we had to find the age of Aman, or Rahul, we could have
found both.
So, let's see, what all we can derive from a question.
First, let's see the first line.
Aman will be 4 times the age of in 6 years.
So, we have to find the present age of Aman.
Let's change the color of the pen.
Let the present age of both of them, be A years.
Why am I writing A years?
So that you can understand the relation between A and R.
That is why I am denoting it.
You can take anything.
So, let the present age of Aman be A years.
And similarly, let the present age of Rahul be R years.
What is the present age of both of them?
Now, let's see the relation in the second line.
If the age of Aman is 7 times the age of Rahul,
The age of Aman is 7 times the age of Rahul.
This is one relation in the present age.
And the relation in the first line is,
Aman is 4 times the age of Rahul.
When? After 6 years.
So, first of all, we will see,
After 6 years,
What will be the age of Aman?
Let's suppose my age is 20 years now.
So, after 6 years, my age will be?
Obviously, 20 plus 6 is 26 years.
So, similarly, if Aman's age is A years now,
What will be Aman's age after 6 years?
Aman's age would be?
Aman's age after 6 years?
Aman's age will be A plus 6 years.
Whatever is his present age,
If we want to see, we will add the present years after 6
years.
That will be his age after 6 years.
Similarly, what will be Rahul's age after 6 years?
Rahul's age will be R plus 6 years.
Now, his age is R.
After 6 years, his age will be R plus 6 years.
Now, this is the relation after 6 years.
What is the relation given in that?
That time, Aman's age is 4 times of Rahul's age.
So, in both these cases, the relation is given.
That is, Aman's age after 6 years,
That is, A plus 6, 4 times of age of Rahul,
Which is Rahul's age after 6 years.
So, A plus 6 is equal to 4 into R plus 6.
So, you have two equations.
One is in red and the other is in red.
In both the equations, there are two unknown variables.
That is, A and R.
So, there are two equations and two variables.
You can easily find out their solution.
So, how will we do it?
Simply, put A's equation in the second equation of R.
So, we will put A is equal to 7R here.
So, what will happen? 7R plus 6 is equal to 4.
Multiply it inside.
4R plus 24.
Got it?
Now, solve like terms together.
R and R terms together and constant terms together.
So, 4R will go here.
Minus will go here.
So, this would be 7R minus 4R.
That is, 3R.
So, you will get 3R is equal to...
Now, 6 is plus here.
It will go there and become minus.
So, 24 minus 6 is equal to 18.
Now, 3 is in multiply.
It will go there and become divide.
So, R will become 18 by 3.
And 18 by 3 is equal to 6.
So, R will become 6.
What was R?
R was Rahul's present age.
So, R is equal to 6 years.
So, how much will be Aman's age in present? 7 into R.
That is 7 into 6.
So, what will be A's value? 7 into 6.
Sorry.
That is 42 years.
So, how much is Aman's present age? 42 years.
And how much is Rahul's present age? 6 years.
So, you got his present age.
If you were not asked about his present age in the same
question, you would have been asked about his present age.
What will be his age after 6 years from today?
So, obviously, in present age, add all the years that are
asked.
For example, 6 years from today.
So, add 6 years to Aman's age, which is 42 years.
So, you will get his age after 6 years.
Similarly, if you ask about his age 6 years ago, you will
get his age minus.
So, your concept should be clear that you will always take
the present age.
And if you talk about future, you will add the same number
of years.
If you talk about past, you will subtract the same number
of years.
Because you were young before. So, we will add and subtract
for the past.
These were easy questions.
This much explanation was required in the first question.
Rest of the questions will not require so much explanation.
And we will also solve them quickly.
Look at the second question.
We have A and B's average age is 66 years.
So, what is the concept in this question?
It is a question of age.
Along with this, we have the question of average.
That is, this is also a question of average.
Usually, we do the question of age in the topic of average.
But, let's do it in this topic.
So, A and B's average age is 66 years.
Now, recall the topic of average.
What is average?
Average is the total number of marks in 5 subjects.
And we have to find the average marks of that student.
So, we will add the marks of total subjects.
And divide all the terms that we are adding.
If we are adding from 5 subjects, then divide it by 5.
Similarly, if there are 2 people in the class.
So, first add the marks of those 2 people.
And divide the marks of all the terms that you are adding.
So, A and B's average age is 66 years.
So, let the age of A be A year.
Let the present age of A be A year.
And the present age of B be B year.
So, A and B's average age is 66 years.
This is the first line.
Then, the average age of A, B and C.
Earlier, there were only 2 people.
Now, there is one more person.
That is, C person.
Now, their average age is 66 years.
But, now the average age of 3 is 55 years.
So, for the average age of 3, we will sum the age of all 3.
And divide it by 3.
So, what do we get from the second line?
We have taken the age of A.
We have taken the age of B.
Now, let us take the age of C.
So, the age of all 3 is 55 years.
This is the second line's formula.
Next, what is the age of C? So, we have to find the age of
C.
So, what do we do?
In the previous question, we were substituting the value.
For example, in the first equation, we had relation between
A and R.
So, we had put A in terms of R in the second equation.
Similarly, here also, we have given the value of A plus B.
Here also, we have given the value of A plus B.
So, from here, we can substitute the value of A plus B.
So, what is the value of A plus B?
The value of A plus B is 66 into 2.
So, from 2 to 2, we get 12.
So, we get 132.
Now, if we take the value of A plus B,
So, what will we get?
If we substitute the value of A plus B,
Now, the unknown is only C.
We have to find the value of C.
So, C will be multiplied by 3.
So, 132 plus C is equal to 55 into 3.
So, this is 15, 115, 165.
Now, if 132 is in the plus sign,
So, what will happen after subtracting?
So, minus 132.
So, what is the value of C?
The value of C is 3.
2 out of 5 is 3.
3 out of 6 is 3.
So, 1 out of 1 is 0.
So, the value of C is 33.
Whose age was C?
C was the age of the person.
So, we wanted the same age.
So, what is the age of C?
That is 33 years.
What is the age of C? 33 years.
So, this question was also easy.
Similarly, let us see the next question.
See the next question.
Now, what type of question is this?
We have taken the average.
Now, see what is being used in this?
The ratio is being used.
20 is to 7.
The ratio is being used in this question.
So, let us see.
A father is four times as old as his son.
So, let us take the age of the father.
Let the age of the father be X years.
Let the age of the son be Y years.
A father is four times as old as his son.
So, X is the age of the father.
Which is four times of son's age.
That is 4 into Y.
So, this is the first equation.
X is equal to 4Y.
Then, 8 years hence, the ratio of father's age to the son's
age will be 20 is to 7.
That is 8 years after 8 years.
So, this was the present.
After 8 years, what will be the age of the father?
The present age will be X plus 8 years.
Similarly, what will be the age of the son?
The age of the son will be Y plus 8 years.
You can write it as father's age plus son's age.
I am writing it in short.
Father's age will be Y plus 8 years.
After 8 years, the ratio of father's age to the son's age
will be X plus 8 into Y plus 8.
Which is equal to 20 is to 7.
Now, what to do?
You can write the ratio in fraction.
X plus 8 into Y plus 8 is equal to 20 is to 7.
Now, we have two equations.
First equation is X is equal to 4Y.
Second equation is this equation.
In this equation, we will substitute the value of X in
terms of Y.
That is X is equal to 4Y.
We will substitute here.
We will cross multiply and we will get the answer.
We will substitute 4Y in place of X.
4Y plus 8.
7 will be multiplied here.
7 will be here.
Y plus 8 will be multiplied here with 20.
Y plus 8.
Now, only Y is there in this equation.
In one equation, we will subtract the value of unknown.
7 into 4Y is equal to 28Y.
7 into 8 is equal to 56.
This is equal to 20 into Y is equal to 20Y.
20 into 8 is equal to 160.
Now, solve these like terms together.
20Y will be here.
So, minus 20.
8Y is equal to 160 minus 56.
160 minus 56 is equal to 4.
5 minus 5 is equal to 104.
This is equal to 104.
What is the value of Y?
Y is equal to 104 by 8.
104 by 8 is equal to 8.
1 times 8 is equal to 24.
3 times 8 is equal to 24.
So, Y is equal to 13 years.
Y was the age of the Sun.
Y is equal to 13 years.
Now, what is the sum of their present ages?
Y is equal to X.
We need the sum of both the ages.
Y is equal to 13 years.
The value of X is 4 x 13 4 x 13
If you add both of them because we need the sum 4 x 13 plus
13 that would be 5 x 13 so 13 x 5 will be 15 and 5 x 5 will
be 65 so their sum will be 65 years
In present their age sum is 65 years
I hope this question will be clear to you
Do not do anything in ratio
Ratio means you have to convert it in simple fraction
Then how will you solve?
First substitute the value
There are two equations
With the help of two equations
Substitute and make one equation in one variable and solve
it and find out the answer
Let's move to the next question
Let's see the next question
Whose answer is this?
Proportion Till now the ratio was of two people
Now it is of three persons
The present ages of three persons are in the proportion 4 x
7 x 9
There are three persons
Let those three persons also take
Let's take PQR
Now in which proportion is PQR?
Let's take P
Let's take Q
Let's take R
So in which proportion is the ratio of these three persons?
In 4 x 7 x 9
Now 8 years ago the sum of their ages was 76 years This is
present present age present age
Now we have to find 8 years ago 8 years ago
What will be the age of P?
Obviously P minus 8 8 years ago 8 years ago, the age of P
will be less
What will be the age of Q?
Q minus 8
What will be the age of R?
R minus 8 8 years ago, the sum of their ages was 76
So their sum was 76
Then find their present age Simply, their sum is 76
So what will be this?
If we add, then P plus Q plus R is equal to 76
And how many times is 8 from here? 8 minus 8 minus 8 minus
8, that is minus 24 Minus 24 will go here, so what will be
the result?
Plus 24
So this is your 100 So P plus Q plus R is equal to 100
What is this? P is present age of P
Q is present age of Q and R is present age of R Now we have
this relation
And we will subtract one relation from this
When all three are given in this proportion then they will
be equal to some quantity
Let that quantity be equal to K So what is the age of P? P
is equal to 4K Similarly, Q is equal to 7K Whatever they
are, we have to multiply them by K
And what is R? 9K So this PQR value in terms of K you will
put here
This is called common ratio
If any one of them is equal then we will take that equal
thing as constant
So all these will be multiple of K Corresponding ratio is
given
For P, it is 4K
For Q, it is 7K
For R, it is 9K
So R becomes 9K
Now put the value here
So 4K plus 7K plus 9K is equal to 100
So add all the lag terms 9 plus 7 is equal to 16 16 plus 4
is equal to 20 20K is equal to 100 0 to 0 is cancelled 1 to
2 is cancelled
So what is the value of K? 5 When K is equal to 5 then put
the value of K in PQR
Then we will get the age of P
Q and R So let us find the age of P
So let us find the age of P
You have the age of P
Let me write it with another pen You have the age of P 4
into 5 that is 20
Age of P is 20
Age of Q is 7 into K that is 7 into 5
Age of Q is 35
And what is the age of R? 9 into K that is 9 into 5 which
is 45 So age of P is 20 years Age of Q is 35 years
And what is the age of R? 45 years at present
So we have easily tackled this question Now moving on to
the last question Now moving on to the last question I told
you that these will be easy questions
There is no much theory for this We just have to apply
basic maths So see the question
The sum of ages of 5 children The sum of ages of 5 children
born at 3 year interval each is 50
The sum of ages of 5 children The sum of ages of 5 children
born at 3 years of interval
Decode this line Decode this line We have 5 children
Let us take 5 children
Let us take 5 children 1 is A 2 is B 3 is C 4 is D 5 is E
How many children are born in each interval?
For example
If A is born in 2000
B is born in 2003
C is born in 2006
Because there is 3 year gap between their birth year
Similarly D will be born in 2009 in 2012.
So which is the oldest child in them? A because he was born
first.
So this is your eldest child and this is your youngest
child because he was born last and he was born first.
Then how old is the youngest child? Youngest child is the
age of E person.
So we use sum of ages of 5 is 50.
Now how will you apply this? If we want to find out the age
of the youngest child, then we use the sum of ages of X.
So we use X as the present age.
So this is X years.
So D is the age of X plus 3 years.
Similarly C is 3 years older than D.
So X plus 3 plus 3 years.
So C is X plus 6 years.
Similarly B is X plus 6 plus 3 years.
So X plus 9 years.
So A is X plus 9 plus 3 that is X plus 12 years.
So this is the present age and the sum of the present age
is 50 years.
So how will you add? You will add like terms
X values and constant terms.
So you have 1X, 2X, 3X, 4X, 5X.
So 5X is added that is 5X plus 12 plus 9 plus 9 is 21.
21 plus 6 plus 3 is 9 that is 30.
So sum 30 is equal to 50.
30 is taken there.
5X is equal to 20.
X is taken in 5 divided.
20 by 5 that is 4.
So the youngest child is 4 years old.
So 4 years X is his age.
Similarly the youngest child is 4 years old.
So D is 4 plus 3 is equal to 7 years.
I hope you have understood the age questions and you will
be able to tackle all the age related problems.
We will meet in the next video. Thank you for watching the
video.
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