Get the ratio and proportion concepts right

Hyderabad: In this series of articles, we will look at how to solve the questions on Ratio and Proportion, which is one of the essential topics for State government recruitment tests. 1. Direct Proportion: If increase/decrease in an observation x shows an increase/decrease in observation y, amount x and y are said to be directly […]

Hyderabad: In this series of articles, we will look at how to solve the questions on Ratio and Proportion, which is one of the essential topics for State government recruitment tests.

1. Direct Proportion: If increase/decrease in an observation x shows an increase/decrease in observation y, amount x and y are said to be directly proportional to each other.

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If x and y are directly proportional, they can be represented in the form of x y

x = k y (k is a constant)

Example (1): The cost of one chair is Rs 450. Then the cost of 4 chairs is Rs 2,250.

As the number of chairs increase, their cost also increases.
The number of chairs and their cost are directly proportional.
Example (2): In a = 5b, it is clear that if b = 1,2,3 ……….
The value of a = 5,10,15,……

Here if b increases, then a also increases

a and b are directly proportional.

2. Inverse Proportion: If the increase/decrease in an observation x shows an decrease/increase in observation y, amount x and y are said to be inversely proportional to each other.
If x and y are inversely proportional, they can be represented in the form of x 1/y
x = k × 1/y (k is a constant)

xy = k

Example (1): If 2 men can do the work in 10 days, then 4 men can do the same work in 5 days.

As the number of persons increase, the number of days decrease

The number of men and days are in inverse proportion.

Example (2): If a = 7/b, it is clear that b = 1,2,3,….

the value at a = 7/1,7/2,7/3,…..

Here if b increases, a decreases

a and b are inversely proportional.

Continued proportion:

If a, b and c are three numbers such that a : b = b : c then these numbers a, b and c are said to be in continued proportion.

If a : b = b : c then b² = ac

Here, b is said to be the mean proportional to a and c, and c is said to be the third proportional to a and b.
Example: 7 : 14 : : 14 : 28

Important points:
If a, b and c are three numbers such that a : b = b : c

i.e., a/b = b/c, then

i) b² = ac

ii) b/a = c/d
iii) a/c = a²/b²
iv) a/c = b²/c²

v) a/c = (a² b²) / b² c²

IMPORTANT POINTS :

1) If a : b = c : d then ad = bc

2) a/b = (c am)/ (d bm) if and only if c/d = a/b

3) If a/b = c/d = e/f = g/h = ……….= k, then (a c e g)/(b d f h) = k

4) If a/b = c/d, then

i) Invertendo = b/a = d/c

ii) Alternendo = a/c = b/d
iii) Componendo = a b/b = c d/d
iv) Dividendo = a-b/b = c-d/d
v) Componendo and Dividendo = a b/a-b = c d/c-d
4. If a/b = c/d = e/f = …………….= k, then (xa/b yc/d ze/f ….)/ (xb yd zf …) = k

5. If a/b = c/d = e/f = …………….= k, then (a² c² e² ….) / (b² d² f² …..) = k

Golden ratio:

The golden ratio is a special ratio between two quantities in which the ratio between the two quantities is equal to the ratio of their sum to the larger of the two quantities.
Golden Ratio is indicated with —–
—— = 1.6180339887.

To be continued…

M.Venkat
Director

MVK Publications

Dilsukhnagar

7671002120