Ratio 1 | CAT Preparation 2024 | Arithmetic | Quantitative Aptitude
Summary
TLDRIn this educational video, Ravi Prakash introduces the concepts of ratios, proportions, and their applications in mathematics. He explains the literal meaning of ratios, using examples like dividing 56 rupees between two people in a 4:3 ratio. Prakash further delves into combining ratios and illustrates how to find the combined ratio of multiple variables. He also discusses methods for converting ratios with fractions into whole numbers for easier calculation. The video serves as a comprehensive guide to understanding and applying ratios in various mathematical problems.
Takeaways
- 📚 The class focuses on the concepts of ratios, proportions, and their applications in mathematics.
- 🔢 Ratios are expressed as A:B and can be understood as dividing a quantity into parts according to the ratio.
- 💡 The script explains how to distribute a sum of money, like 56 rupees, among two people based on a given ratio.
- 📈 An example is provided to illustrate how to calculate the distribution of 171 rupees between two individuals with a ratio of 11:8.
- 🌐 The importance of maintaining the same multiple for each part when distributing according to a ratio is emphasized.
- 🔄 The script demonstrates how to simplify ratios by canceling out common factors to make calculations easier.
- ➡️ A method to combine multiple ratios is introduced, which involves aligning and adding the parts of each ratio.
- 🧩 The concept of finding a combined ratio when given separate ratios for different pairs of items is explained.
- 💡 The script teaches how to convert ratios involving fractions into whole numbers by finding the least common multiple (LCM).
- 📝 A practical problem-solving approach is showcased, where the distribution of money is calculated based on given ratios and conditions.
Q & A
What is the basic concept of a ratio as explained in the script?
-A ratio is a way to compare two or more quantities. It is written in the form 'a to b', which means 'a' is to 'b' as in the fraction 'a/b'. It can also represent how a whole is divided into parts, such as dividing 56 rupees into two persons 'a' and 'b' in the ratio of 4:3.
How does the script illustrate dividing money in a ratio?
-The script uses the example of dividing 56 rupees between two persons 'a' and 'b' in the ratio of 4:3. It explains that if the total parts are 7 (4+3), each part is worth 56/7 = 8 rupees, so 'a' gets 4 parts (32 rupees) and 'b' gets 3 parts (24 rupees).
What is the meaning of 'k' in the context of the script when dealing with ratios?
-In the script, 'k' is used as a variable to represent a common multiple that scales the ratio parts. For example, if 'a' gets 7 parts and 'b' gets 9 parts, 'a' can be represented as 7k and 'b' as 9k, where 'k' is the common multiple that, when multiplied by the ratio parts, gives the actual values.
How does the script explain combining ratios?
-The script explains combining ratios by aligning the parts that correspond to the same entity across different ratios. For example, if 'a' has a ratio of 7 to 'b' and 'b' has a ratio of 8 to 'c', then 'a', 'b', and 'c' can be combined into a single ratio by making 'b' the common part and adjusting 'a' and 'c' accordingly.
What is the significance of the least common multiple (LCM) in combining ratios?
-The LCM is significant in combining ratios because it helps to convert the parts of the ratios into whole numbers, which are easier to work with. By multiplying each part of the ratio by the LCM of the denominators, the fractions are converted into integers, simplifying calculations.
How does the script handle ratios where the parts are not whole numbers?
-The script suggests converting the fractional parts of a ratio into whole numbers by multiplying by a common factor, typically the LCM of the denominators of the fractions, to make the calculations simpler and more straightforward.
What is the strategy for solving problems where ratios are given as fractions?
-The script recommends converting the fractional ratios into whole numbers by multiplying with the LCM of the denominators. This conversion simplifies the problem-solving process, making it easier to apply the concepts of ratios and proportions.
How does the script demonstrate the application of combined ratios in a problem?
-The script demonstrates the application of combined ratios by solving a problem where a certain amount is distributed among 'a', 'b', 'c', and 'd' in a given ratio. It shows how to find the individual amounts by understanding the combined ratio and using it to set up equations that can be solved for the values.
What is the method to find the individual values when given a combined ratio and a condition like one value being less than another?
-The script suggests setting up the combined ratio and then using the given condition to find the difference in parts. By understanding the value of one part (unit) of the ratio, the individual values can be calculated by multiplying the number of parts each entity has by the value of one part.
How does the script approach a problem involving ratios and ages?
-The script approaches age-related ratio problems by first finding the combined ratio of the ages and then using the given age difference to determine the value of one unit of the ratio. By multiplying the number of units each person has by the value of one unit, the individual ages can be calculated.
Outlines
📚 Introduction to Ratios
Ravi Prakash introduces the concept of ratios, explaining that ratios are a fundamental topic with applications in various mathematical chapters. He uses the example of dividing 56 rupees between two people, A and B, in the ratio of 4:3. The division is broken down into parts, where the total parts (7) are calculated, and then each part's value is determined. The ratio is represented as A parts to B parts, and the value of each part is calculated based on the total amount divided. The paragraph emphasizes the literal meaning of ratios and how they are used to divide quantities.
🔢 Understanding and Combining Ratios
This section delves into the concept of combining ratios. Ravi uses an example where different amounts are divided between A, B, and C in various ratios. He explains how to find the combined ratio by aligning the parts of B in both ratios and then determining the equivalent parts for A and C. The process involves finding the least common multiple (LCM) to make the comparison easier. The paragraph also discusses how to combine multiple ratios by following a pattern where the numerators and denominators are combined sequentially to form a new ratio. This method is applied to solve a problem involving the distribution of money among A, B, C, and D, with a given condition about the difference between B and D's shares.
🧩 Applying Ratios to Problem Solving
The paragraph focuses on applying the concept of ratios to solve a specific problem where the ratio of amounts with A, B, C, and D is given as 3:4. Ravi demonstrates how to calculate the individual amounts by first determining the ratio values for each person and then using the given condition that B gets 30 less than D to find the value of 'K'. Once 'K' is found, the amounts for A, B, C, and D are calculated by multiplying their respective ratio units by the value of 'K'. The solution is presented in two methods, providing clarity on how to approach ratio problems.
🎓 Combining Ratios with Age Problems
This part of the script applies the concept of ratios to solve age-related problems. Ravi presents a scenario where the ages of A, B, and C are in the ratio of 2:7:9 and 12:8:11, respectively. He shows how to combine these ratios to find the individual ages by first aligning the common ratio part (B) and then calculating the equivalent age units for A and C. The problem is solved by determining the value of one age unit and then calculating the ages of A, B, and C based on their respective units. The paragraph concludes with a clear explanation of how ratios can be used to solve age problems.
🔄 Converting Fractional Ratios to Integers
The final paragraph discusses how to handle ratios given in fractional form, such as 1/2:1:4:1/5. Ravi explains that it's often easier to convert these fractions into integers to simplify calculations. He demonstrates how to find the least common multiple (LCM) of the denominators to convert the ratios into whole numbers, making the problem easier to solve. The paragraph emphasizes the importance of converting ratios to a simpler numerical pattern to facilitate problem-solving.
Mindmap
Keywords
💡Ratio
💡Proportion
💡Variation
💡Fraction
💡Distributing
💡LCM (Least Common Multiple)
💡Combining Ratios
💡Numerator
💡Denominator
💡Units of Ratio
Highlights
Introduction to the concept of ratios and their significance in mathematics.
Explanation of how to write ratios and their application in fractions.
Practical example of dividing 56 rupees between two persons in a 4:3 ratio.
Understanding how to calculate the value of each part in a ratio.
Demonstration of distributing 171 rupees between two persons in an 11:8 ratio.
Clarification of the meaning of ratios through the division of money.
Introduction to the concept of combining ratios.
Methodology for combining ratios of different quantities.
Explanation of how to find the combined ratio of A:B:C when given separate ratios.
Technique to combine multiple ratios using a systematic pattern.
Application of ratio combination in solving a problem involving distribution of money.
Solution to a problem where the ratio of ages is given and one person is older by a certain number of years.
Method to convert ratios with fractions into whole numbers for easier calculation.
Strategy for solving problems when ratios are given in fractions and how to simplify them.
Conclusion and summary of key points about ratios and their applications.
Transcripts
[Music]
hi everyone my name is Ravi Prakash and
welcome to the first class of ratio
proportion and variation okay so we'll
start with the ratios will start with
ratios okay it's a very good topic and
its application is in other chapters
also so ratios okay see in fraction if
it is a by B in ratio it is written as a
H to be right if you're not going higher
mathematics these are literal meaning of
fraction okay a by B is in the ratio of
A to B okay same thing right so they
like we're dividing something let's say
if I'm dividing 56 rupees fifty six
rupees in between two persons a and B in
the ratio in the ratio for each two
three so what we actually think actually
thinking is that 56 is divided into
total 4 plus 3 7 parts okay what we're
actually thinking is 56 strip rupees is
divided in to total 7 parts okay
one part is rupees 56 sorry seven part
is replace 56 okay the seven parts is
replaced 56 so one part of this ratio is
rupees eight if one part is rupees 8 so
for part is rupees 32 4 into 8 32 and
three part is 3 into 8 24 right this is
a literal meaning of ratio so I'm
dividing something let us say 56 rupees
in the ratio 4 is 2 3 in bitter 2 in
between two persons a and B okay so that
means a is getting 4 parts and B is
adding three parts so total seven parts
is to be distributed okay out of those
seven parts those survived value of the
seven part is equal to how much is equal
to 56 rupees if that seven part is equal
to 56 rupees so one part is equal to
rupees eight one part is rupees they
tried so one part of ratio represents
represents rupees eight
so for part is 32 three parts is 24 okay
now
similarly suppose editing is some other
number it's do it quickly actually okay
so let's say this 171 I'm distributing
evident to persons a and B in the ratio
in the ratio 1182 it such that a is
getting eleven part and B is getting
eight parts so here same thing in total
11 PERT plus 819 parts right total 11
Plus 8 19 parts is equal to rupees 171
so 1991 71 that means one part is equal
to rupees nine if one part is rupees
nine so eleven part is replaced 99 and
eight part is what rupees 72 8 into 972
right so 99 plus 72 is 171 okay this is
the meaning of ratio okay meaning of
ratios so what we actually do is what we
actually do suppose and dividing rupees
fifty six or rupees let's any example
with fifty sixty four in between two
persons in the ratio of a and B in the
ratio of seven eight to nine so now what
you do so I because the ratio increase
in the same same multiple right that
means if a is getting seven parts and B
is getting nine parts this is a ratio
okay so they can a can that means a will
get a multiple ultimate what ultimate
number will be a will be getting in a
multiple of seven that is 7 K and B will
be getting in a multiple of nine eight
is nine K there's a meaning of it right
7 k + 9 0 16 K is equal to 64 so k is
equal to 4 right so k is equal to 4 so a
gets that means k equal to 4 so a hits
how much a gets 7 into 428 and B gets 9
into 436 this is the fundament it ok so
this always write this K and K should be
same ratio ratio increases same multiple
right that means basically see how the
ratio comes if I'm cancelling right 10
by 15 so a has 10 rupees B has 15 Rubio
- the ratio 10 by 15 okay
a has ten rupees and B has 15 rupees so
the ratio is ten by fifteen if I cancel
by 5 2 y 3 so I get okay I say ok 2 is
to 3 ratio but I have cancelled by same
amount right so if I can if I want to
come back to 10 in 15 I have cancelled
by 5 so this is 2 into 5 this is also 3
into 5 so this is nothing but this is
nothing but 2 K and 3 K if something is
in the ratio of 2 to 3 I can assume is
that 2 as given as 2 X + 3 X or 2k + 3
kids okay this variable should be same
correct now come to the main point
now suppose suppose this a is to be some
amount is divided among a is to be
between a is to be is in the ratio 7 is
to Kate okay and some amount is divided
between B and C in the ratio 12 H to 13
so from here I want to get what is the
ratio what is the ratio of combined
ratio of H to be H to see what is the
combined ratio of H to be to see right
so quite easy to do it actually we say
okay if a has got if a has got 7 then B
is 8 if B is 12 this a is 13 right so
what we assume here we assume that okay
what is B so let B be a number B right B
is the same in today here but
representing two different numbers 8 and
12 8 and 12 right so I'll try to make it
same so that number can be same at their
LCM or let's say phone I can simply
multiply right because it will it arrive
a result from there also so 8 down let's
say B is what B is 8 into 12 okay so how
much a will become so for a for a B is 8
and for a B has become 12 times that
means a will also be with a a will also
become 12 times right what is a 7 into
12 right now for C for C B is 12 and for
C B has become 8 times
so C will also become a time that is 13
into it as the ratio right so what is H
2 B 2 C here so a is 2 B hoc is nothing
but 84
- 96 h2 1:04 okay now here it's Edwin
cancel the common ratio ready to cancel
at common ratio so it will be cancelled
by I think through - so 42 48 and 52
another time into that is 21 24 and 26
therefore a is to be hit to see is what
21 8 to 24 H - 26 right that means total
suppose a is getting 21 parts in B is
getting hit in 24 parts and see is
getting 26 parts right very important
point to combine two ratios okay now see
on the same pattern we can combine
multiple ratio I can combine multiple
ratio as well right for example let's
say a is 2 B is some 2h 2 3 okay
B - C is some 4 h - 5 C is 2 D is 6 6 to
7 and take one more like T is 2 e is 8
is 2 9 try to 92 combine it right what
is the ratio of or I can write here
itself what is the ratio of a is 2 B a
is 2 B is to C is 2 B is 2 e what is the
ratio C now we discuss this point in the
last video right suppose only 2 ratio is
given H to be 1/2 H 2 3 and B is to C
was 4 is 2 5 so what is the ratio of A
to B to C so a is 2 B to C is what no B
here is 2 3 B here is 4 so I take B as 3
into 4 so a becomes what a becomes 2
into 4 and C becomes 5 into 3 so this if
you observe here what is a here a is 2
into 4 a is 2 into 4 that is combination
of all the numerator numerator means if
I had 2 to 3 as 2 by 3 and 4 is 2 5 x as
4 by 5 so 2 & 4 here are the numerators
okay so a is like 2 into 4 B is now
first denominator and second numerator
that is three into four
okay so B is 3 into 4 and C is again 3
to 5 all the denominators okay this is a
general pattern in pattern into ratios
we can find It button in three ratios
then for each was right so that's why
we'll write directly here those with
that pattern a here is like 2 into 4
combination of all numerators so if I
did if I write 2 is 2 3 s if I write 2
is 2 3 s 2 by 3 this is 4 by 5 then this
has 6 by 7 and this is 8 by 9 okay so
what is a basically so a is combination
of all numerators Attis a is 2 into 4
into 6 into T this is value of a 2 into
4 into 6 into it right now listen
carefully very carefully for B how will
you write for B how will you rate for
like B I shifted right I shifted here
one place here and 3 into 4 that is
first denominator and next numerator so
here since B will combined all the four
ratios so if I shift here so B will be 4
denominator that is 3 deliberated and
left all numerators that is 3 into 4
into 6 into it so B is 3 into 4 into 6
into 8 4 C now for C now C C for C or do
you shift again 1/4 see you again shift
1 again shift 1 mins first to
denominator and next to numerators that
is 3 5 6 and 8 so C will be 3 into 5
into 6 into 8 4 D again same thing you
shift one more that means 4 3 numerator
denominator and large numerator that is
3 5 7 8 so D will be 3 5 7 8 3 5 7 & 8
what does e will be all all all the
denominator that is put a large ratio
here laughter sure is see oil derivative
that is 5 into 3 put a last ratio here 3
into 5 into 7 to 9 so E is what 3 into 5
into 7 into 9 so very important point we
have discussed here how to combine
multiple ratio
just make it a pattern here okay just
make it a pattern how to make a pattern
first is a okay first is gay what is a a
is the combination of all numerators so
a is the combination of all numerators 2
4 6 8 right now for B shift one short
one means first denominator and next
three numerators that is 3 4 6 8 for C
shift one more that also be right for XI
for C shift one more that is first first
2 denominator and next to numerator that
is 3 5 6 8 okay
for D shift one more that means first 3
denominator and last numerator that is 3
5 7 and 8 and for e if you shift one
more that automatically becomes all the
denominator that is 3 5 7 8 3 5 7 and 9
okay
so quickly you can make one example here
quickly right thing in mind suppose a is
2 B is 5 H 2 8 ok B is to C is 7 is 2 9
C is 2 D is for H 2 11 and B is 2 e is
is 7 is 2 or the strain is DeMayo to
repeat the number to get you confused
here and D is - he is what - is to 13 so
what is the ratio of a is 2 B is to C is
2 D is to e what is the ratio what is a
year basically all the numerators that
is 5 7 4 2 so a is 5 into 7 into 4 into
true it is be here all the no shift 1
for B shift 1 first eliminated and next
3 numerator set is eight seven four to
eight seven four two four C shift one
more that is first two denominators and
last two numerator that is 8 9 4 2 4 C 2
V 8 9 4 2 8 into 9 into 4 into 2 48 will
be again shift one more that means
basically shift 1 Mormons
first three numerator and the
denominator
eight nine eleven to so T will be eight
nine eleven - 8 9 11 - but he will be if
you shift one more all the denominators
right that is 8 9 11 and 13 so very
important concept it is very important
concept it is okay I hope it is clear
enough now see will apply this in a
question will apply this in a question C
question
a by B equal to B by C equal to C by D
is equal to 3 by 4 now if if B gets
rupees 3 0 head less than D okay find
the amounts with a b c and the okay so
question is some amount is distributed
among a b c and d such that K by B equal
to B by C equal to C by D equal to 3 by
4 okay this is given a by B equal to B
by C equal to C by D equal to 3 by 4 so
if B gets rupees 3 0 8 less than D what
is the value of a B C and D that is how
much amount is with ABC and D C what is
it what is this mean here this means
that a is 2 B is also 3 8 2 4 okay B is
to C is also 3 8 2 4 right and C is 2 D
is also 3 8 2 4 so I can quickly get a
ratio of ABCD a/b c/d
what is a here a here what is a is all
numerators 3 into 3 into 3 so a is 27
now B by shifting 1 that means what is
be first in weight denominator and next
row next two numerators so 4 into 3 into
3 so B is how much B is 36 okay third
one what is C here C is first two
denominator and next numerator that is 4
into 4 into 3 that is 48 notice B here B
is all all denominators that is fall
into fall into 4 64 this is a ratio of A
to B CH 2 CH 2 B so that means basically
now if I solve in this and ratio what
does mean that begets rupees 3 0 8 less
than D that means difference of B and D
is rupees 3 0 we understand difference
of B and D is how much rupees 3 0 8 that
basically means that what a difference
of B and D here in ratio it is 28 units
I can rake in ratio to 28 units or 28
parts right so in ratio difference of B
and D is how much 28 units or 28 parts
and those 28 units is equal to how much
rupees 3:08
okay so what is the ratio of oil value
value of ratio of 1 unit therefore one
unit of ratio is what it is 3:08 by 28
that is rupees 11 so if one minute a one
unit ratio is a rupees 11 for ratio what
is the value of a so a is how much a is
27 into 11 a is 27 units one unit herb
is relevant so 27 into 11 is rupees 297
this is the answer for a B for B 37 into
11 okay B has got 37 you 36 units so B
is 36 units
one unit is rupees 11 the 36 into 11
rupees 396 right
si si has got 48 units so 48 into 11 si
has got rupees 528 and D has about 64
units 264 into 11 DL Gautama trapeze
7:04 this answer right 297 396 528 and
7:04 it's a very good question and a
nice application of that concept here
okay it's a good question correct call
the method 2 will be now or the method 2
also again think of what is method 2 in
method 2 again same it's at least same
thing method to get assume this as a has
got 27 K so a has got 27 K B has got 36
K C has got 48 K and D has got 64 K now
difference of B and D so 28 K is equal
to rupees 3:08 same thing k equal to xi
k equal to 11 right so that's basically
the same thing you assume some K or X or
not that's basically the same thing
right
just to give you both conceptual clarity
I hope it is clear
yeah okay next one next one C ratio of
Ages of a is 2 B is 7 8 to 9 and ratio
of edges of B is to C is basically 12 H
to 11 okay 12 8 to 11 so if if C is 12
point 5 years elder than a elder than a
then find individual ages of a B and C
find individual ages of a B and C so you
can solve this question of easily I
think the ratio of a is 2 B is what it
is 7 to 9 okay
Joby's to see 12 is 12 and right so you
can write in the same line a is to B is
to C so a gets to B is to C it is H to
be 7 is to 9 and B is to C is 12 is to
11
what is the combined ratio so I can take
B as what 9 and 12 so B is what 9 into
12 what is C then 11 into 9 4 c b has
become 9 x + 4 a B has become 12 times
so what is b eh7 into 12 left cancel the
count on out here cancel 3 year in
cancel 3 3 4 John 3:3 J + 3 3 J what is
this become it becomes 28 is 236 8233 11
3 or 33 3 into 12
3632 for 28 right so ratio of a B and C
is how much 2836 and 33 simply in mind
now you can do you can do it now C is
12.5 years elder than a so C is in ratio
5 minutes elder than it so 5 units of
ratio is equal to 12.5 in years that
means one unit of ratio is equal to how
much 2.5 years that's it so you got the
area of a now what is the age of day so
age of a is how much age of a is how
much 28 units so 28 into 1.5 years
it's 28 into one four five front went
well is how much 42 years 28 + 28 to
half 14 42 years what is the age of B
now 36 years 36 units 36 into 1.5 years
that is 36 and half 18 that is 54 years
but is the age of C now 33 units to 33
in to 1.5 how much it is 33 and half
fifteen point five forty nine point five
years this is the answer a is B a and C
right so you will clear this concept
okay it's a very good concept of
combining ratios for this is like 413
ratio how
to combine multiple ratios okay now
suppose suppose sometimes the ratio is
given as a is to B is to C is half is to
1 by 4 is to 1 by 5 okay and some amount
every divide between a B and C so what
we can do normally is we can assume
amounts as it's a right ABC has a
half-ish to 4 1 by 4 is to 1 by 5 so I
can take okay a has 1/2 K that is K by 2
B has K by 4 and C has ky5 right if a -
B - C is in the ratio of 2 is to 3 to 4
that means 2 K 3 K 4 K so it is in
fraction doesn't matter into K into K
into K okay but this will be linear so
we'll not prefer this method does it
will end there right so what is the best
way to convert this fractions to convert
these fractions into integers to convert
this fractions into integers right that
means this a is 2 B is to C can be
multiplied with right there common
numbers to convert them into integers by
what number to multiply to multiply with
the number which will cancel - 4 and 5
so LCM of 4 and 5 all the right common
multiple of 4 and 5 2 4 and 5 so 2 + 4
sm is for only 4 and 5 what is I the
same 20 so multiply by 20 20 20 20 what
you look at will get ABC as 10 is 2 5 8
2 4 so this is the same ratio this is
the same ratio as 1/2 is 2 1 by first to
5 right this is much easier to solve
this is much easier to solve in fraction
it is difficult to solve capital
calculation will be more right that
means always convert to this new
numerical pattern and solve the question
ok wherever it is given in fractions
right okay
so we'll continue all the concepts of
ratio in the next video thank you
[Music]
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