Math Guide

Proportional Type

Introduction for proportional type:


Proportion is defined as two terms equality any one term in proportion .a fourth proportional for numbers a,b,c a number d such that a/b=c/d. Let us consider cost of a chocolate is Rs. 2, then the cost of 5 pens is Rs. 10 and the cost of 8 chocolate is 16 . Now for the ratio of two quantities is 5: 8 will be further the ratio of their costs is 10: 16.Consider any proportion and verify yourself whether the product of extremes is equal to theproduct of means. 

 Then the proportion is 5: 8 =10: 16. 


Proportional Type - Example Problems: 


 Main property for proportion is product of extremes = product of means 

 when we use above property to check whether the given 4 quantities are in right proportion. and also we can find the missing term of a proportion if 3 of its terms are given, 

Example 2:3 =6:9 


 Proportional type - Example 1: 


The cost of 3 balloons is 24 and the cost of 6 balloons is Rs. 48. What is the proportion? 

 Solution :The ratio of two quantities = 3 : 6 

The ratio of their costs = 24 : 48 

The proportion is 3 : 6 = 24 : 48


 Proportional type - Example 2

Verify 3 : 4 = 9 : 12 is a proportion or not. 

 Solution :Product of extremes = 3 × 12 = 36Product of means = 4 × 9 = 3636 = 36These two products are equal.3 : 4 = 9 : 12 is a proportion.


 Proportional Type - Example 3

 If 2 × X = 3 × Y, find X : Y

 Solution :`2 x X` = `3 x Y` 

 Divide both sides by 2`(2 xx X)/2` =`(3xxY)/2` 

 ` X =3/2 Y`Divide both sides by Y` X/Y`` = `` (3Y)/(2Y)`=`3/2``X : Y = 3 : 2`


 Proportional type - Example 4

If the cost of 7m cloth is Rs. 49, find the cost of 5m cloth.Quantity (in m) Cost (in Rs.)7 495 ? 

Solution:The proportion is7 : 5 = 49 : ? 

Product of means = 5 × 49 = 245 

 Product of Extremes = `7 x ?``7 x ?` = 245 

 ` (7 xx?) /7` = `245/7`= `245/7`=35 

 The cost of 5 m cloth = Rs. 35.


 Proportional type - Example 5

If `2 : 5 = 6 : ?` is a proportion, find the missing term. 

 Solution :Product of extremes =` 2 x ?`

 Product of means = `5 x 6 = 30.`Since it is a proportion, 

`2 x ?= 30`Divide both sides by 2`(2 xx ?)/2` = `30/2` = 15