Ratios proportions mixtures and alligations concept detailed video explanation.

1. Ratios Proportions Mixtures
and Alligations

2. Ratios Proportions Mixtures and Alligations
• Ratios Proportions is a very important concept. Thus it has many
practical applications and uses in daily life. Mixtures and Alligation is
also a subset of ratios and proportions. Hence, we should learn these
concepts very well. But before moving further, we will first
understand the concept of percentages. Percentages is a very
important concept and is a necessity while understanding concepts
such as SI-CI, ratios proportions, mixtures alligations etc.

3. Percentages in ratios and proportions
• The term percentage means parts per 100 or “for every hundred”. It is
widely used concept in ratios and proportions . A fraction whose
denominator is 100 is called percentage and the numerator of the
fraction is called the rate percent. Thus, when we say a man made a
profit of 20 percent we mean to say that he gained Rs.20 for every
hundred rupees he invested in the business, i.e., 20/100 rupees for
each Rupee. The abbreviation of percen is p.c. and it is generally
denoted by %.

5. Percentages in ratios and proportions
• The term percentage means parts per 100 or “for every hundred”. It is
widely used concept in ratios and proportions . A fraction whose
denominator is 100 is called percentage and the numerator of the
fraction is called the rate percent. Thus, when we say a man made a
profit of 20 percent we mean to say that he gained Rs.20 for every
hundred rupees he invested in the business, i.e., 20/100 rupees for
each Rupee. The abbreviation of percen is p.c. and it is generally
denoted by %.

6. How percentages work
• Let’s start with a number X (= 1 X)
X increased by 10% would become X + 0.1 X = 1.1 X
X increased by 1% would become X + 0.01 X = 1.01 X
Similarly, X increased by 0.1% would become X + 0.001 X = 1.001 X
X decreased by 10% would become X – 0.1 X = 0.9 X
X decreased by 1% would become X – 0.01 X = 0.99 X
Also, X decreased by 0.1% would become X – 0.001 X = 0.999 X
X increased by 200% would become X + 2X = 3X
X decreased by 300% would become X – 3X = –2X

7. Important points to remember
• Also, let us remember that:
2 = 200% (or 100% increase), 3 = 300% (or 200% increase), 3.26 = 326% (means 226% increase),
fourfold (4 times) = 400 % of original = 300% increase, 10 times means 1000% means 900%
increase,
0.6 means 60% of the original means 40% decrease, 0.31 times means 31% of the original means
69% decrease etc.
1/2 = 50%, 3/2 = 1 + 1/2 = 100 + 50 = 150%, 5/2 = 2 + 1/2 = 200 + 50 = 250% etc.,
2/3 = 1 - 1/3 = 100 - 33.33 = 66.66%, 4/3 = 1 + 1/3 = 100 + 33.33 = 133.33%,
5/3 = 1 + 2/3 = 100 + 66.66 % = 166.66%, 7/3 = 2 + 1/3 = 200 + 33.33 = 233.33%,
8/3 = 2 + 2/3 = 200 + 66.66 = 3 - 1/3 = 300 - 33.33 = 266.66% etc.
1/4 = 25%, 3/4 = 75%, 5/4 (1 + 1/4) = 125% (= 25 increase), 7/4 (1 + 3/4 = 2 - 1/4) = 175% (= 75%
increase), 9/4 (2 + 1/4) = 225% (= 125% increase), 11/4 = 275% = (175% increase).
1/5 = 20%, 2/5 = 40%, 3/5 = 60%, 4/5 = 80%, 6/5 = 120%, 7/5 (1 + 2/5) = 140% etc.
1/6 = 16.66%, 5/6 = 83.33%, 7/6 (1 + 1/6) = 116.66%, 11/6 = 183.33%
1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%, 7/8 = 87.5%, 9/8 = (1 + 1/8) = 112.5%, 11/8 = (1 + 3/8) =
137.5%, 13/8 = 162.5%, 15/8 = 187.5% etc.
1/9 = 11.11%, 2/9 = 22.22%, 4/9 = 44.44%, 5/9 = 55.55%, 7/9 = 77.77%, 8/9 = 88.88%, 10/9 =
111.11%, 11/9 = (1 + 2/9) = 122.22% etc.

8. Variations and Proportions Basic Concepts
• Direct proportion :
If two quantities X & Y are related such that any increase or decrease in ‘Y’
produces a proportionate
increase or decrease in ‘X’ or vice versa, then the two quantities are said to be
in direct proportion.
In other words X : Y = X/Y = k (a constant)
or X = KY or Y = K’X (where K and K’ are constants)
X is directly proportional to Y is written as X ∝ Y or X = K Y
• Inverse proportion :
Here two quantities X & Y are related such that, any increase in X would lead to a
decrease in Y or
any decrease in X would lead to an increase in Y. Thus the quantities X & Y are
said to be inversely
related and X is inversely proportional to Y is written as
X ∝ 1/Y or X = k/Y or XY = k (constant) or the product of two quantities remains
constant.