Types of proportion for grade 8.

a) Direct proportion.

b) Indirect proportion.

c) Compound proportion.

Direct proportion:

If we are given two quantities and with the increase (or decrease) of one quantity the other quantity also increases (or decrease). We say that the quantities are indirect proportion with each other.
Example:
If a dozen bananas cost for $ 4.5. How many bananas can be bought with $30?
The proportion becomes;
4.5 : 12 :: 30 : x
means = extremes
4.5 x = 12 ´ 30
x = (12 ´ 30) / 4.5
x = 80
80 bananas can be bought with the given amount of money.

Indirect proportion:

If the quantities are in such a way that due to increase in one the other decrease or due to decrease in one the other increase then the proportion is said to be in indirect proportion.

Example:
1) If 14 diggers can dig a tunnel in 10 days. 28 workers will complete the same job in how many days?
Days        Workers
10             14
 x              28
here unlike direct proportion we can not write;
10 : x :: 14 : 28
but here the situation is;
10 : x :: 28 : 14
x = (28 * 14) / 10
x = 39.2 days.

so we conclude that in case of indirect proportion we find a proportion such that should:
If w, x, y, z are the four ratios then they must always satisfy,
w : x :: z : y

2) If car is traveling on a speed of 70 km/hr covers a distance in 1:30 minutes. What speed the same car is required to have for covering the same distance in 1:15 minutes.
Speed          Time
  70               90
   x                75

x : 70 :: 90 : 75
75 x = 70 * 90
x = 6300 / 75 = 84 km/hr

Compound proportion:

In many practical situation we need to deal with more than one proportion. Like in previous example we could also require the distance covered along with the speed and time. In such cases there is a mutual relationship in the ratios. The compound ratios can be both direct and in direct.
Example:

1) If 15 students complete 90 questions in 3 hours. How long it will require 16 students to complete 48 questions?
Time Questions Students.
3hr 90 15
xhr (direct) 48 (direct) 16 (indirect)

Means = Extremes
x * 90 *16 = 3 *15 * 48
x * 1440 = 2160
x = 1.5 hrs.

 

 

 

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