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Ratio and Proportion

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Ratio

source: bpexam.blogspot.com Fig: Ratio
source: bpexam.blogspot.com
Fig: Ratio

The ratio shows the relative sizes of two or more values. The ratio compares two or more quantities of the same unit. It tells how many times quantity is less or more than another quantity of the same unit.

For example, The ratio of a to b = a:b or \(\frac{a}{b}\). Similarly ratio of b to a = b:a or\(\frac{b}{a}\). The quantities of a ratio are called the terms of the ratio. The term in the numerator is called antecedent and the denominator is called consequent.

Proportion

source: www.mathx.net Fig: Proportion
source: www.mathx.net
Fig: Proportion

If there is the equality between two ratios then it can be known as the proportion. Let a, b, c and d are called first, second, third and fourth proportional respectively, The first and fourth proportional are called Extremes. The second and third proportional are called Means.

Types of proportion

  1. Direct Proportion

    source: www.math-for-all-grades.com Fig: Direct Proportion
    source: www.math-for-all-grades.com
    Fig: Direct Proportion
    If the ratio of the number of articles and their cost is equal then it is called direct proportion. If the number of articles increases or decreases and their cost also increases or decreases. For example,
    The cost of 1 articles = Rs.15
    Then, the cost of 5 articles = 5× Rs.15 = Rs.75
    ∴ Ratio of the number of articles = 1:5
    The ratio of cost of pens = 15:75 = 1:5
  2. Indirect Proportion

    source: slideplayer.com Fig: Indirect Proportion
    source: slideplayer.com
    Fig: Indirect Proportion
    If the ratio of the number of workers and the ratio of their working days are exactly opposite then it is called indirect proportion. For examples,
    1 man can finish a piece of work in 20 days. Then 2 men can finish the same work in 5 days.
    Here the ratio of the number of men = 1:4
    the ratio of the working days = 20:5 = 4:1



  • The ratio tells how many times quantity is less or more than another quantity of the same unit.
  •  The term in the numerator is called antecedent and the denominator is called consequent.
  • The first and fourth proportional are called Extremes.
  • The second and third proportional are called Means.
.

Very Short Questions

Solution:

Let, the required cost be Rs x.

Here, the quantities of apples and their cost are in direct proportion.

\(\therefore\) 8:5 = 180:x

or, \(\frac{8}{5}\) = \(\frac{280}{x}\)

8x = 5 × Rs 280

x = \(\frac{5 ×Rs 280}{8}\) = Rs 175.

So the required cost is Rs 175.

Solution:

Here, Rs 2 is the tax for the income of Rs 100

Re 1 is the tax for the income of Rs \(\frac{100}{2}\) = Rs 50

Rs 525 is the tax for the income of Rs 525 × 50 = 26250.

So, the required income of the man is Rs 26250.

Solution:

In 8 days, Hari can do 1 work.

In 1 day, Hari can do \(\frac{1}{8}\) part of the work.

In 6 days, Hari can do \(\frac{6}{8}\) parts of work = \(\frac{3}{4}\) parts of the work.

Now, remaining parts of the work = (1 - \(\frac{3}{4}\)) = \(\frac{1}{4}\) part of the work.

So, Gopal finished \(\frac{6}{8}\) parts of the work.

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  • A ratio is equal to 5 : 7. If the antecedent is 25, what will be its consequent?

    30
    40
    45
    35
  • If the terms 2, 3 and 14 are in proportion, then what will be its fourth proportional?

    23
    22
    24
    21
  • If the terms 6, 8, and 24 are in proportion, find the third proportional?

    15
    18
    17
    16
  • What will be the value of x if 8 : 10 = x : 50

    10
    40 
    30
    20
  • If the 12, 60, 40 terms are in proportion, what will be its second proportional?

    8
    11
    10
    9
  • Find the ratios and reduce 2kg and 250g in their lowest terms.

    4 : 3
    5 : 2
    8 : 1
    1 : 4
  • What will be the results when dividing Rs 60 in the ratio of 1 : 4?

    Rs 72, Rs 120
    Rs 12, Rs 48
    Rs 15, Rs 21
    Rs 12, Rs 44
  • The ratio of two numbers is 7 : 2. If the greater number is 28, what will be smaller one?

    12
    8
    16
    2
  • If the pair of complementary angles are in the ratio 2 : 3, find them?

    54°, 126°
    20°, 45°
    36°, 54°
    40°, 80°
  • 60 boys in a hostel have provisions for 30 days. How long would the provisions last to 72 boys?

    25 days
    45 days
    15 days
    35 days
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