# 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