Today we are going to talk about some important arithmetic formulae on PROBLEM BASED ON AGES , which is very important for types of competitive examination. Students are advised to learn these formulae and keep practicing with it.

**SOME IMPORTANT SUTRAS**

1). If t yrs earlier , the age of the father is x times the age of his son. At present time , the age of father is y times the age of his son. Then their present age ;

son age = t(x-1)/x-y , father age = y[t(x-1)/x-y] years respectively.

2). If the present age of the father is x time the age of his son, t years later , the age of father become y times the age of his son , then their present age ;

Son age = x[t(y-1)/x-y] and father age = t(y-1)/x-y

years respectively.

3). If t1 yrs earlier , the age of the father is x times the age of his son. and hence t2 years later, the age of father is y times the age of his son. Then their present age ;

Son age = t1(x-1)+t2(y-1)/x-y , and father age =

t1y(x-1)+t2x(y-1)/x-y

4). If the ratio of the present age of A and B is x:y, and m years earlier, their ratio are a:b , then equation of solution is; ,, x-m/y-m = a/b

5). If the ratio of the present age of A and B is x:y, and m years laters, their ratio are a:b , then equation of solution is; ,, x+m/y+m = a/b

6). If m years earlier, the ratio of the age of A and B is x:y, and n years later, their ratio are a:b , then equation of solution is; ,, x+n+m/y+n+m = a/b

7). If the ratio of age of A and B is a:b and sum of their ages is S , their ages is ;

age of A = Sa/a+b , and age of B = Sb/a+b

8). If M is as smaller than N , as he is greater than P , and sum of ages of N and P is S , such that P<M<N , then the age of M is = S/2

This chapter contain limited no of formulae , the best way to deal with such type of questions is that , you have to learned to make equations by given data in one or two variables and solve it by proper methods.