Proportions

Summary

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Proportion
If the ratios between quantity A and quantity B is equal to the ratio between quantity C and quantity D, then the four quantities A, B, C and D, are said to be in proportion. Proportion is denoted by the signs '∷’ or ‘=’. 

Thus, the quantities 4, 16, 5 and 20 can be written as 4:16∷5:20 or 4:16 = 5:20.

The order of the terms in a proportion carries value. The quantities 4,16, 5 and 20 are in proportion, whereas 4, 20, 5 and 16 are not in proportion.

In the proportion a:b∷c:d, the quantities a and d are the extreme terms, and b and c are the middle terms.

Unitary method
The method of calculating the value of one unit and using this value to calculate the value of the required number of units is called the unitary method.

For example, suppose the cost of 8 bags is Rs 240. Now, to find the cost of 6 bags, using the unitary method, we first find out the cost of one bag. 

Cost of one bag = 240 8 = Rs 30

Now, the cost of 6 bags = 6 × 30 = Rs 180

Hence, the cost of 6 bags is Rs 180.

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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.

Sol:
Given that 4 ,x,9 are in continued proportion then

? 4 / x = x / 9

? x 2 = 36...

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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