## Aptitude Chapter-2

Bodhak competitive bank exams ages in this chapter we will discuss AGES AND AVERAGES. We will see how o solve through equations and through shortcut methods.

AGES : In Ages after or hence means +(add)  and Ago or before means –(subtract)

In ages we take present ages. Example : Present age of Father(F),Mother(M),Daughter(D),Son(S) etc.

In ages writing an equation is important.

#### competitive bank exams ages

Four years ago the sum of the ages of the father and son is 60.

The equation as follows :

F-4+S-4=60.

Example :

The present age of a father is 3 years more than 3 times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of father?

A) 30

B) 33

C) 36

D) 39

Solution :

1:  By the 1st statement F=3+3S.

2: from the 2nd statement F+3=10+2*(s+3)

by solving above 2 equations

F=3+3S

F+3=10+2x(S+3)

3+3S+3=10+2S+6

3S+6=2S+16

3S-2S=16-6

S=10.

F=3+3(10)=3+30=33

### AVERAGES:

Average=Sum of the observations/number of observations

Sum=average*number

If Average increased by including one person or number than the number or person is more than average & by excluding one person or number than the number or person is less than the average.

If Average Increases by excluding one person or number than the number or person is less than the average &

excluding one person or number than the number or person are more than average.