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Concept of Ratio

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definition

Ratio: The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. This method is known as ratio.

notes

Ratio:

i) Comparison by taking difference:

In our daily life, many times we compare two quantities of the same type. If the height of Rahim is 150 cm and that of Avnee is 140 cm then, we may say that the height of Rahim is 150 cm – 140 cm = 10 cm more than Avnee. This is one way of comparison by taking the difference.

ii) Comparison by division:

In many situations, a more meaningful comparison between quantities is made by using division, i.e. by seeing how many times one quantity is to the other quantity. This method is known as comparison by ratio.

Consider an example. The cost of a car is 2,50,000 and that of a motorbike is 50,000. If we calculate the difference between the costs, it is 2,00,000 and if we compare by division; i.e. `(2,50, 000)/(50, 000)` = 5: 1.

Thus, in certain situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is the Ratio.

  • The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. This method is known as ratio.
  • Mathematical numbers used in comparing two things that are similar to each other in terms of units are ratios.

  • We denote ratio using symbol ‘:’

  • A ratio can be written in three different ways viz, m to n, m: n, and mn but read as the ratio of m is to n. Example: 2: 3 = ratio of 2 is to 3.

  • Note that the ratio 3: 2 is different from 2: 3. Thus, the order in which quantities are taken to express their ratio is important.

  • For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.

  • A ratio may be treated as a fraction, thus the ratio 10 : 3 may be treated as `10/3`.

  • A ratio can be expressed in its lowest form. For example, ratio 50: 15 is treated as `50/15`; in its lowest form `50/15 = 10/3`. Hence, the lowest form of ratio 50: 15 is 10: 3.

Same ratio in different situations:

Ratios can remain the same in different situations.

  • The length of a room is 30 m and its breadth is 20 m.
    So, the ratio of the length of the room to the breadth of the room =`30/20=3/2`=3: 2.

  • There are 24 girls and 16 boys going for a picnic. The ratio of the number of girls to the number of boys = `24/16=3/2`= 3: 2

The ratio in both examples is 3: 2.

Example

Ratio of distance of the school from Mary’s home to the distance of the school from John’s home is 2: 1.
(a) Who lives nearer to the school?
(b) Complete the following table which shows some possible distances that
Mary and John could live from the school.
Distance from Mary’s home to school (in km.)
10   4    
Distance from John’s home to school (in km.)
5 4   3 1
 
(a) John lives nearer to the school (As the ratio is 2: 1).
(b)
Distance from Mary’s home to school (in km.)
10 8 4 6 2
Distance from John’s home to school (in km.)
5 4 2 3 1

Example

Find the ratio of 90 cm to 1.5 m.

The two quantities are not in the same units. Therefore, we have to convert them into the same units.
1.5 m = 1.5 × 100 cm = 150 cm.
Therefore, the required ratio is 90: 150.
= `90/150 = (90 xx 30)/(150 xx 30) = 3/5`.
Required ratio is 3: 5.

Example

There are 45 persons working in an office. If the number of females is 25 and the remaining are males, find the ratio of:
(a) The number of females to the number of males.
(b) The number of males to the number of females.
Number of females = 25
Total number of workers = 45
Number of males = 45 – 25 = 20
Therefore, the ratio of number of females to the number of males = 25: 20 = 5: 4
And the ratio of number of males to the number of females = 20: 25 = 4: 5.
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Shaalaa.com | Word Problems On Ratio Part - 1

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Word Problems On Ratio Part - 1 [00:10:12]
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