Hello everyone, welcome back to a new video.
In today's video, we are going to continue the topic of
Ratio and Proportion, which we did in the last video.
We did all the related terms that were used in that video.
And what did we do? We read their formulas, what all are
used and where.
Today we will do questions based on that.
But before starting the questions, let me tell you one more
small topic.
We have learnt the definition of Ratio and Proportion.
One more word that you hear in this, you can hear it as
Proportional.
That one thing is proportional to another thing.
You can hear one word like this.
And you can hear the other word as Inversely Proportional.
What will be the meaning of these two? Let me tell you
quickly.
Proportional means, if we have two quantities, two things.
So if I tell you the relation between them, I will say A is
directly proportional to B.
So A is directly proportional to another quantity B.
If we say A is directly proportional to another quantity B.
So what will be the meaning of this? We will denote it like
this.
A is directly proportional to B.
We will write it like this.
And what will be the meaning of this?
A is equal to, if we want to remove the sign of
proportionality and write it as equal to.
So like we used to write in ratio, we have to do the same
in this.
So equal to any constant, let us suppose k is that constant.
A is equal to constant into B, where k is any constant.
So if we are given about directly proportional, that two
things are directly proportional.
That means they are each other's constant multiple.
What happened to A? A is multiplied by B.
And if we take k here, it will be multiplied by k.
If we are multiplying A by 1 by k, we are getting B.
Or if we are multiplying B by k, we are getting A.
So both of them are each other's multiple.
Because they are getting by multiplying.
Now if it is directly proportional, then what will be the
meaning of that?
The changes that will come in A, the same changes will come
in B also.
Because they are happening with equality.
So if A will increase in something, then B will also
increase at that time.
Like in this example, I will give you the distance, time
and speed values.
If we have any formula, distance is equal to speed into
time.
We have this.
So what is there in this? We have distance.
If I say any of these things as constant.
Let us suppose I am saying that the speed of the vehicle is
constant.
It is constant throughout.
So let us take k as constant.
So what will happen? d is equal to kt.
What does this mean?
If I go backwards from this step, this will make d is
directly proportional to time.
Means distance is directly proportional to time.
If our distance increases, then what will be the time to
cover it?
Time will also increase.
Means it will take more time to cover more distance.
Did you understand this much?
So this is the example of directly proportional.
Next is inversely proportional.
What will we call inversely proportional?
We will say that any quantity p is inversely proportional
to q.
Another quantity q is inversely proportional.
So what will we do?
What is inverse? 1 upon q is reciprocal.
So p is directly proportional.
Is this visible?
If p is inversely proportional, then 1 upon q.
We will write inversely proportional like this.
If p is inversely proportional to q, we will write p is
inversely proportional.
1 upon q.
Inversely proportional means it is inversely proportional.
Inverse means reciprocal.
So p is inversely proportional to q.
Or p is directly proportional to 1 upon q.
What does this mean?
The opposite of the changes in p will come in q.
If p increases, then q decreases.
So I will explain this example with distance.
If I write this,
Speed is equal to distance upon time.
This will be the formula.
If I take d as constant, means we have constant distance.
So if I put k instead of d, then I get k.
If I write this backwards,
S is directly proportional to 1 upon t.
S is inversely proportional to time.
This means if the speed of any vehicle is increasing, then
obviously it will take less time to reach there.
If the speed is slowing down, then it will take more time.
So inversely proportional and proportional have this
relation.
I hope you have understood this much.
This is the only topic you had left to learn.
Next we will do Inkay based questions.
Inkay based questions as in ratio-proportion based
questions.
So your first question is,
See this, read the first question.
If a ratio b is equal to 5 ratio 9, and b ratio c is equal
to 7 ratio 4, then find a ratio b ratio c.
How will we do this?
What is a ratio b given to us? a ratio b is given to us as
5 is to 9.
We have converted this ratio into fraction.
Similarly, we will write b ratio c as b by c is equal to 7
by 4.
Now what we have to find?
We have to find the ratio of all three.
That is a ratio b ratio c.
In both the terms, what is common?
We have b common.
See here also we have b and here also we have b.
And how is it common?
It is in the denominator and this is in the numerator.
It is not that it should be in the denominator or numerator.
So what we have to do in this case?
Whatever is common, we have to make it same.
If we do that a value is 5, it should be 5k.
But now I will say in general.
Let us suppose that it is 5.
And b value is 9.
Similarly, b value is 7 here and c value is 4 here.
So what we will do?
First of all, we will make b common.
We will make it same in both the places.
So if we want to make it same, then take their LCM.
To make it same, take 7 and 9.
7 and 9 are prime numbers.
That means they do not have any common factor.
So what we have to do?
We have to multiply this by 7.
And we have to multiply this by 9.
Then both of them will become same.
Now if I am multiplying by 7 here, then I am changing this
ratio.
But you cannot change the ratio.
You cannot make a mistake with it.
Except you can divide by the same thing.
So if you have multiplied by 7 here, then you have to
multiply by 7 up here also.
Here you have multiplied by 9.
So you have to multiply by 9 down here also.
So what will be the value of a by b? 35 divided by 9 into 7
is 63.
Similarly, 9 into 7 is 63 and 4 into 9 is 36.
So b value is same.
If you put the same value in a, b, c, then a value is 35.
Now moving on to, ek baar dekh liye screen shot waqeera jo
bhi likhna hai kap le liye.
Next moving on to next question that is this, if x ratio y
is equal to 3 ratio 4 then 7x plus 3y ratio 7x minus 3y is
equal to.
Kaise karenge? Kaise kar sakte hain? x ki yeh value dekar
agar aur y ki yeh value 4 dekar aap rakh ke nikal sakte
hain? Theek hai ek tarika aapka woh jayega woh to easiest
way hai karne ka ki x ki value yeh rak do 3 and y ki value
4 rak do usme aur ratio
woh solve karke nikal lo.
But humne ek cheez seekhi thi componendo and dividendo wala
case.
Wo uska issamaal hum kaise karege questions mein jo maine
aapko batana chahati thi is question ke madhyam se wo
seekhte hain.
Yeh dekhe componendo and dividendo mein kya tha? Agar
humare paas a by b hai to yeh a by b is equal to c by d hai.
To isko hum kya kar sakte the? Isko hum a plus b and a
minus b is equal to c plus d c minus d.
Yeh humne seekha tha componendo and dividendo mein.
To same hum yaha dekh rahe hai ki dekho agar upar humare
paas kya hai agar yeh to ek alag cheez ho gayi to a by b
humare paas kiske equal ho jayega? a plus b divided by a
minus b.
To agar humare paas yeh 7 x plus 3 y divided by 7 x minus 3
y hai.
Isse compare karo ki do same quantity plus ho rahi hai.
Wahi dono same quantity neeche subtract ho rahi hai.
To yeh agar hum backwards jayenge to yeh backwards mein kya
dekha humein? a upar and b neeche.
To matlak jo aage wali term hai wo upar ho jayegi that is 7
x divided by jo peeche wali add ya subtract ho rahi hai wo
denominator mein a jayegi 3 y.
To yeh kya ho jayega? Humein kya nikalna hai? Humein kuch
aur nahi.
Hum agar yeh nikal denge to humein iska ansar mil jayega.
To yeh kya hogaya? 7 x upon 3 y humein nikalna hai.
Ab aap 7 x aur 3 y kaise nikalenge? To dekhiye yeh humaare
paas x solution x ratio y inko fraction mein likhlo x by y
is equal to 3 is to 4.
Ab humein kya chahiye? Humein chahiye 7.
7 chahiye agar mein 7 ko multiply and divide kar doon.
To same cheez hogaya.
To 7 ko multiply kar diya humein
divide karenge y ke saath bhi.
But mein 7 ko y ke saath divide karne ke bhajaye.
Kyuki humein y ke saath 3 chahiye.
Main usko agar 7 ko agar main yaha pe multiply karti.
Ya main isko cross multiply kar doon.
Its one and the same thing only.
To main sideh next step kar rahi hoon.
That is main kya kar rahi hoon? 7 ko instead of multiplying
with y, main usko idhar 3 ke saath multiply kar.
I hope yeh aapko clear hoga.
Main achche se likhar bata deti hoon ki maine kya kiya hai.
Chalo step wise bata deti hoon.
Ki 7 se multiply and divide karenge yeh to sabko pata chal
gaya.
Next step mein 7 ko idhar le jaah rahi hoon kyuki humein y
ke saath 3 chahiye.
7 nahi chahiye.
To yeh ho jayega 7 x divided by y aur yeh 7 idhar cross
multiply mein 3 ke saath chala jayega.
To 7 x 3 divided by 4.
Teeke. To humein numerator mil gaya 7 x.
Ab humein next cheez kya chahiye? 3 y.
To 3 y ke liye kya karenge? 3 ko y se multiply karenge.
And se multiply karenge to upar bhi karna padega.
Y se karenge to upar 7 x se bhi karna padega.
To wo 3 mein idhar multiply karne ke bajaya usko cross
multiply kar rahi hoon with 4.
To 3 idhar karenge and into 3 idhar karenge.
To yeh humare paas kya aajaayega 3 y ki value.
Ab isko solve kar lo to yeh solve karke 3 3 cancel ho gaya.
Yeh aagaya humare paas 7 x upon 3 y ki value kya aagaya
humare paas? 7 by 4.
Ab usme yeh rule laga do.
Humein a b mil gaya.
7 x and 3 y.
Humein c and d mil gaya.
7 and 4.
Thek hai yeh implies tha.
Humein c and d mil gaya 7 by 4.
To value kar isko componento and dividendo jab hum karenge.
To yeh ban jayega.
This would be 7 x plus 3 y divided by 7 x minus 3 y is
equal to 7 plus 4 divided by 7 minus 4.
To yeh aagaya humare paas 11 by 3.
To inka ratio.
Ratio mein jab isko convert karenge yeh already shortest
form mein hai.
To wo kya ho jayega? 11 ratio 3.
Agar aap 3 value dalte jo main aapko first easy case batari
thi.
Agar aap usse karte to aapka kya answer aata hai? Ek baar
karke dekhiye ki x ko aap 3 put kije and y ko 4 put kije.
To 7 x 3 kya ho jayega? 7 x 3 21 plus 3 x 4 12 divided by 7
x 3 21 minus 12.
To yeh kya ban jayega?
Humare paas 3 x 3 x 33 divided by 9.
33 x 9 isko short form mein convert karo.
To 3 x 3 is equal to 7 x 3 is equal to 7 x 3 is equal to 7
x 3 is equal to 7 x 3.
To yeh aapka video pause kariye question padhiye and usko
khud se ek baar solve karne ke koshish kariye.
Fir yeh resume kariye video and dekhiye.
So the question says the average of 11 numbers.
Idhar kiska bhi concept aagaya? Idhar average ka bhi
concept aagaya.
To aapke zaruri nahi hai ki ek concept ke ek hi type ki
question banenge.
Baaki ke concept ko bhi submerge karke ek question bana
sakta hai examiner.
For sure.
To the average of 11 numbers is 36.
Matlab 11 numbers ka average kya hai? 36.
Average ka matlab kya ho gaya? 11 numbers ke average ka ki
agar humare paas suppose 1 se lekar 11 ta koi number hai.
Koi numbering de di.
Jaise de dete x1 x2 upto aise x9 x10 and x11.
These are our 11 numbers.
Inka agar hum sum karenge sum of x1 plus x2 plus x11 tak
aur usko 11 se divide kar denge.
To yeh humare paas nikal ke kya aajaega? Average of these
11 numbers.
Wo kiske equal given hai? Hume 36 ke equal given hai.
To yeh hume mil raha hai is first wali line se.
Whereas average of 9 of them is 34.
In 11 me se agar hum 9 numbers ka average le to wo hume kya
given hai? 34.
To agar hum second line se dekhe to hume second line wale
se kya mil raha hai? x1 plus x2 plus upto x9 divided by 9.
Kyuki average nikal rahe hai to jitna upar sum, jitni
quantities ka hum upar sum karte hain usse se divide karte
hain is equal to hume kya mila? 34.
This is jo bhi hume details mil rahi hain questions se.
If the remaining 2 numbers, ab 9 numbers ka to hume yeh
average mil gaya.
Baaki jo 2 number bache that is x10 and x11.
x10 aur x11 are in the ratio 2 is to 3.
To ek aur information jo hume ne grab kari x10 ratio x11 is
equal to 2 ratio 3.
Likte ja na, saare information pehle question padte hain.
Find the value of smaller number between these 2.
Matlab hume smaller number batana hai between x10 and x11.
In dono me se kaunsa number smaller hoga.
To wo find out karne ke pehle jo iska common ratio hoga wo
hum find kar denge ki that is x10 by x11 yeh kis ratio mein
hai? 2 by 3 ya agar hum common ratio le lenge k
common ratio k le lenge
So, x10 will be 2k and x11 will be 3k.
So, what we have to do is, if we know the value of this k,
then we will multiply x10 and x11 and find out and then we
will tell which number is big and which number is small.
Okay? Now, see, what we will use for this?
Now, this above x1 plus x2 up to x11, it will have 9 sums
also.
It means, this value will also be there.
If I open it and write, then here x10 will also be there in
plus.
In plus, x9 will also be there, plus x8 and so on.
So, if I make it short down, then we can subtract this
value and put it from here.
Right? The value of x1 plus x2 up to x9, we can find out
from here and put it in this.
So, what will be the value of this? x1 plus x2 plus x3 up
to xn.
Multiply 9 there.
So, if we multiply 9 there, then it will be into 9.
So, what will be this?
9 x4 is 36 and 9 x3 is 27.
27 and 3 is 30.
So, this becomes 306.
It means, the sum of 9 numbers is 306.
Now, put the sum of 9 numbers here.
9 numbers sum plus 10th number plus 11th number divided by
11.
What should we get?
We should get 36.
So, multiply 36 here also.
Sorry, what should I multiply by 36? 11.
I will rub this upper thing.
So, you solve this.
What will this become?
You put these values of x10 and x11, which are in common
ratio.
So, this will become 306 plus x2k plus x3k is equal to 36
into 11.
That is 36 into 11.
6, 9, that is 396.
So, this becomes 396.
Now, add these like terms.
This would be 5k.
And here, 396 minus 306 will become 90.
So, what is the value of k?
90 divided by 5.
How will this cancel out? 1 and 40. That is 8.
So, we have the value of k, which is 18.
We have the value of common ratio, which is 18.
If we have the value of k, then we can find the value of
x10 and x11 also.
So, we will multiply by 2.
2 into 18 will be greater or 3 into 18?
Obviously, 2 into 18 will be greater.
18 into 2 is 36.
So, x10 is smaller.
So, 2 into 18 will be 36.
And x11 will be 3 into 18, which is 54.
So, x10 is smaller.
And what is the value of x11? 36.
So, we have to find the value of x11.
So, x11 will be 36.
So, now you know how to use ratios and proportions.
Moving on to the next question.
Ratios and proportions are very basic questions.
They do not require any hard and fast rules.
You just need to follow the information that you know.
Now, the number to be added to each of the following
numbers to make the number in proportion is?
We have been asked to add a number to all the numbers and
make them in proportion.
Now, when do we say 4 numbers are in proportion?
Remember, when I asked you to write a ratio b in proportion
to c ratio d.
And a by b is equal to c by d.
Then, all these 4 numbers are in proportion.
So, we have to add something to these 4 numbers to make
them in this form.
So, let that number be x.
Then, we will solve.
That is, 7 plus x.
The first number is this.
What is the second number? 16 plus x. What is the third
number? 43 plus x. And d is equal to 79 plus x.
It is equal to a sign because when we add something to it,
the new numbers are in proportion.
So, we have defined the proportion.
Now, cross multiply and find the value of x.
Do it quickly.
You do it in your notebook and I will do it here.
Then, tell me.
So, we will multiply 79 into this whole thing.
7 into 79 is 49.
That is, 553 x plus 7x is equal to 16.
6x is equal to 18.
6x is equal to 45.
6x is equal to 48.
6x is equal to 88.
6x is equal to 88 plus 16x plus 43x plus x square.
What you have to do is, you have to multiply this bracket
here. Then, you will apply distributive law.
For example, 7 plus x into 79 plus x.
First, multiply 7 by the whole bracket.
So, 7 into 79 plus 7 into x.
That is 7x.
Now, multiply x by both sides.
Plus 79x plus x into x.
That is x square.
This is our answer here.
Now, both the sides have terms x square and x square.
So, if we take x square here, it will be equal to minus.
Cancel out.
So, this is our answer.
Next, add like terms.
That is, 79 plus 7x is equal to 86x.
And, 553 is equal to 688.
Plus, these two like terms.
This was 43.
So, this will be 9.
59.
59x.
Now, take the like terms here.
This will be equal to 89x.
86x minus 59x is equal to 688 minus 553.
Solve it.
20 and 16.
That is 727x.
Is equal to 53135.
135.
So, what will be the value of x? 135 divided by 27.
Divide by 27.
So, what will happen?
First, cancel out 3.
Because, 3 is 27.
And, if we add 1 plus 3 plus 5, that would be 9.
So, what is coming?
It comes in the table of 3.
So, we can solve from 3.
That is, 3 times 4 is 12.
And, 15 times 5 is 3 times 9.
So, 9 times 5 is 9.
So, what is the value of x? 5.
So, the number which we have to add to make them in
proportion, that number would be number 5.
So, the answer is 5.
Clear? Now, next question.
Read it first.
A bag contains 10 paisa, 25 paisa and 50 paisa.
I guess, this is a question which is
very old.
Because, money is over.
So, 10 paisa, 25 paisa and 50 paisa coins in the ratio 3 is
to 5 is to 2. We have a bag.
You have a bag or purse.
It is fashionable.
In that, you have 10 paisa coins. And, some 25 paisa coins.
and some 50 paisa coins.
These are the collections.
Now, what is the ratio of those coins?
The ratio of 10 is 3, the ratio of 25 is 5, and the ratio
of 50 paisa is 2.
The order in which it is given to you, in that order only
you will see the ratio.
If 10 is first, then the ratio of 10 is first.
If 25 is first, then the ratio of 25 is in the middle.
Then 50 is of 50.
Let the common ratio be K.
If the common ratio is K, then the ratio of 10 paisa will
be 3K.
The ratio of 25 paisa will be 5K.
The ratio of 50 paisa will be 2K.
Now, making a total of rupees 510, if we sum all the coins,
then the total money we have is rupees 510.
Now, this is in rupees.
And these quantities are in paisa.
So, we have to do conversion.
So, find the number of coins of each type.
So, we have to tell the number of coins of each type.
We have to tell the number of coins.
So, let us suppose, if we have done this, then the common
ratio will be 10.
So, if the common ratio is 10, then the ratio of 10 paisa
will be 3K.
Now, if we have 3 coins of 10 paisa.
3 is the quantity.
But, if we look at it money wise, then how much money are
they giving us? So, if we multiply 10 by 3, then we get 30
paisa.
So, we have to use this.
We have to multiply 3K by 10.
So, 3K into 10.
Because, we are looking at 10 paisa.
We have so many number of coins.
According to 10 paisa, how much money will we get?
Number of coins of 10 paisa into 10 obviously.
Then, the number of coins of 25 paisa.
5K into 25.
Plus, number of coins of 50 paisa into 50.
2K into 50.
How much total amount should we get? That is given.
That is Rs. 510.
Rs. 510.
But, look at this.
We have written all this in paisa.
This is 10 paisa, 25 paisa and 50 paisa.
So, what we have to do is, convert this into paisa.
Or, you can take common ratio of 100K.
Because, we will get by multiplying 100.
Rs. 1 is 100 paisa.
So, I convert this into paisa.
So, Rs. 1 is equal to 100 paisa.
So, how much money will we get in Rs.
Rs. 510 plus 2 into 10.
That much money.
So, now we have same unit on both the sides.
That is in paisa.
So, we can solve this.
3K into 10 is equal to 30K.
Plus, we will write unit later.
Then, 25 into 5.
That is 25.
125K.
Plus, 100K.
Is equal to 510000.
Now, add these like terms.
Then, what will happen? 155 plus 100.
That is 255K.
Is equal to this.
Now, what to do with 255K?
Both are going from 5.
Cancel out.
5 paisa and 5 paisa.
51 paisa.
And, this would be.
Where is it going? 5 paisa.
It will be 0.
Because, 1 is not there.
So, 10 into 2.
And, 2 into 0.
102.
Now, see 51.
It should be cancelled completely.
Because, we have K.
It is quantity.
Number of coins.
So, 51 into 2.
102.
So, 51 into 1.
And, 51 into 2.
102.
So, this is 200.
So, what is the value of K?
The value of common ratio.
K is equal to 200.
So, number of coins.
Individual coins.
So, number of coins of 10 paisas.
3 into K.
That is 3 into 200.
So, how many coins are there of 10 paisa?
I am writing on this side.
Total coins of 10 paisa.
That is 3 into 200.
600 coins.
We have coins of 25 paisa.
5 into 200.
That is 100.
1000 coins.
And, 50 paisa coins.
2 into 200.
That is 400 coins.
So, total number of coins we had to calculate.
That is all.
Now, you can add them up.
If we have 600 coins of 10 paisa.
Then, how much money we have? 6000 will be there.
Then, 25 into 1000 coins.
50 into 400 coins.
These will be in paisa.
You have to add them up.
That will be 5100 paisa.
Okay? So, this question is also done. Next question.
Next question is,
There are many age related problems in ratio and proportion.
So, let's solve some age related problems.
Let's do it.
Look at this question.
Read it once.
So, Seema is 40 years old.
Seema's age is 40 years.
And, Meena's age is 60 years old.
How many years ago?
First, write Seema's age.
40 years.
And, Meena's age is 60 years.
How many years ago was the ratio of their age 3 is to 5?
Means, how many years ago was their ratio 3 is to 5?
So, whatever quantity we are asked, let's suppose.
Let's ask about how many years ago.
So, let's do it.
Let X years ago their age was.
If I ask, If you are 20 years old now, then how old were
you 4 years ago? So, what will you do?
You will write 20 minus 4.
So, you will get to know that you were 16 years old 4 years
ago.
Similarly, if I am asking,
X years ago, X years ago, what was their age?
If their age is this in present, then how old will be X
years ago? So, Seema's age will be X years ago.
40 minus X years.
Subtract all the years that we have asked.
And, Meena's age will be 60 minus X years.
Both of them had this much age one year ago.
Now, at this time, when they are talking about that time,
whatever years they are talking about, at that time, what
was their ratio? 3 is to 5.
Now, we will divide it.
We will write the ratio.
What should it be? 3 is to 5.
That is, 40 minus X divided by, we can also write the ratio
like this.
60 minus X is equal to 3 by 5.
Easy? Your equation will be made.
There is only one unknown, X.
Its value will also be known.
So, multiply this cross.
So, 5 into 40 will be 200.
Minus 5 into X.
5X is equal to 3 into 60.
180 minus 3X.
Solve it.
5X minus 5X will be plus 5.
180 will be minus.
So, it will be 200 minus 180.
20 is equal to minus 3X plus 5X.
If it is a big 5, then it will be 2X.
It will be sine plus.
But, if it is subtracted, then it will be minus.
So, what is the value of X?
The value of X is 20 by 2.
That is 10.
So, 10 years ago, what was their age ratio? 3 is to 5.
What will be Seema's age? 30 years
And what will be Meena's age? 50 years
So if you take the ratio of both
It will be 30 divided by 50 0 to 0 cancel
So 3 is to 5
So our answer is correct
We can also verify
Till now we are practicing
We don't get much time to verify in exam
But till now Our practice session is going on
So what can we do now?
We can verify
In practice session
Whatever mistakes you do
You should be grateful for it
Because the more mistakes you do in practice session
The more you will evolve
And you will get to know
Where were your mistakes
If you keep correcting all
You won't get to know your mistakes
And in exam you will be blunder
I am not saying it will happen to everyone
But sometimes it happens
You won't get to know your mistakes
During your practice session
So mistakes are happening now
No problem
You should not have time for exam
Now last question
This is also age related
So read
If 4 years ago
The ratio between
How many years ago we are talking? 4 years ago
The ratio between the ages of P and Q
Q was 5 is to 3 4 years ago
P Ratio Q was 5 is to 6
And the sum of their ages
At present
At present is 52 years
And the sum of their present age
Is 52 years
What is the ratio of their present age?
So what we will do?
Let's take any age
Let the
Which age we will take?
Obviously we have to take present age
So we will take present age
Let the present age of Let's take P of P be
X years
Means P is
X years
P is
X years
According to question
The sum of their present age
P's present age
P's present age P's present age P's present age Q's Q's sum
is 52
If X is P's age
If we take X, then
Q's present age will be 52 minus X So present age of Q
Present Age of
Q is equal to
Present age of Q is equal to 52 minus present age of P that
is X
So what we have got the present age of P and Q
So we have to find the ratio of these two
So let's see
Like the last question
If their present age is X or 52 minus X
Then what will be their age 4 years ago?
So the data of 4 years ago is 5 is to 6
So what was the age of P 4 years ago?
X minus 4
X is present
So 4 years ago
X minus 4 divided by
Q's age 4 years ago 52 minus X is their present age
We will subtract 4 from it
That is 52 minus X is their present age
We will subtract 4 from it
So 4 years ago age will be 5 is to 6 5 is to 6
So find out
This will be the equation
So this will be 52 minus 4 that is 48 or 48 write here 48
and cross multiply it 6 X minus 6 into 4 24 is equal to 5
into 48 20, 24 minus 5 X
Now take 5 X and bring 24 here 11 X is equal to plus 4, 6
264 So what is the value of X? 264 divided by 11 that is
22, 2's and 44, 4's
So what is X? 24 And what was X?
Present age of P
So the present age of P is he or she
So P is 24 years
And what is the age of Q? 52 minus 24 that is 52 minus 24
that is 28 years
So 28 is the present age of Q
So what we had to find out?
We had to find out the ratio
What is the ratio?
P is to Q
So 24 divided by 28
Cancel out
This is going from 4's table 4 X 6 is equal to 4 X 7 is
equal to 28
So we got the answer 6 is to 7
The ratio of their present age
So I hope all the questions that I have made you practice
in today's class you must have understood them well and
related to them you must have been able to answer the
remaining questions
So we will meet you in the next video with the new topic
Till then keep practicing and study well
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