Ratios

Summary

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Usually, the comparison of quantities of the same type can be made by the method of difference between the quantities.

Ratio
Comparison between the quantities can be made by using division, i.e. by verifying how many times one quantity is into the other quantity. This method is known as comparison by ratio. Ratio can be denoted as ' : ' .
e.g.
Keertana’s weight is 20 kg and her father’s weight is 80 kg. So we can say that Keertana’s father’s weight and Keertana’s weight are in the ratio 20:80.

To calculate ratio, the two quantities have to be measured using the same unit. If not, they should be converted to the same unit before ratio is taken. The same ratio can occur in different situations.

The order in which the quantities are taken into consideration to express their ratio is important. 
e.g.
The ratio 4:5 is different from 5:4. 

A ratio can be treated as a fraction.
e.g.
5:6 can be treated as 5 6.

Equivalent ratios
Two ratios are said to be equivalent if the fractions corresponding to them are equivalent. To calculate equivalent ratio, convert the ratio into a fraction, and then multiply or divide the numerator and the denominator of the fraction by the same number.
e.g.
4:5 is equivalent to 8:10 or 12:15 and so on.

Lowest form
A ratio can be expressed in its lowest form. For example, the ratio 45:25 in its lowest form can be written as follows:
45:25 = 45 25 = 5 x 9 5 x 5 = 9 5 = 9:5
Thus, the lowest form of 45:25  is 9:5.

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1 . Divide: 80 in the ratio 3 : 5

Answer.

(a) Given ratio is 3:5
3 + 5 = 8
Hence the first part = (3/8) x 80 = 30
Second part = (5/8) x 80 = 50

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2 . THE WEIGHT OF 72 BOOKS IS 9KG WHAT IS THE WEIGHT OF 40 SUCH BOOKS

5kg

3 . Find the number when the remainders may be proportional.

Sol:
Assume that x be number subtracted from each of the numbers 54,71,75 and 99 so that the remainders may be proportion.  
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4 . If 4 ,x,9 are in continued proportion find the value of x.

Answer.
Given that 4 ,x,9 are in continued proportion then ? 4 / x = x / 9 ? x2 = 36 ? x2 = 62 Hence x = 6.

5 . By how much must 15 be decreased so that it bears same ratio

Let the number 15 be decreased by x.
According to the given question,
15 ? x : 9 = 20 : 15


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