Ratio and proportion

Divide a given quantity in a given ratio:
Use this formula for finding the share ,
Individual share = (Individual ratio/Total ratio) * Total Quantity
Example: Divide 20 pens between sheela and Anil in the ratio 3 :2
Given ratio = 3:2
Step 1 : find sum of the ratio
Sum of the ratio = 3+2 = 5
Total pens = 20
Individual share = (Individual ratio/Total ratio) * Total Quantity
Step 2 : Use the above formula
Sheela ` s share = (3/5) * 20 = 12
Anil`s share = (2/5) * 20 = 8


Problems:
Mother wants to divide $180 among her sons Ajay and Anoop in the ratio of their ages. If the age of Ajay is 12 years and Anoop is 15 years. Find how many dollars each of them will get?( find the ratio of their ages)

Ray and Rosi started a business and invested capital in the ratio 2 : 3. after one year total profit is divided in the ratio of their invested capital, find the share of each?

Present age of father is 42 years and his son is 14 years. Find the ratio of:
a. Present age of father to the Present age of son
b. age of father to the age of son , when son was 12 years old
c. age of father to the age of son , when father was 30 years old

Divide 60 books in the ratio of 2:3 between John and Kennedy.


Proportion:
When two ration are equal,we can say that thay are in proportional.The symbol is :: ,
a : b :: c : d this means a,b,c and d are in proportional. the condition for proportionality is

Product of means = Product of extremes

Example: check whether 6 , 16,39 and 104 are in proportional or not.
6 : 16 :: 39 : 104 check for this condition Product of means = Product of extremes
16 * 39 =6 * 104
624 = 624 so they are in proportional.
Practice:
check whether 8 , 12 18 and 24 are in proportional or not.
check whether 27, 36,36 and 48 are in proportional or not.