**Basic concepts & Tricks to solve Average Problems**

Here we have given the General Rules to Solve Average Problems. Candidates those who are applied for the various Competitive examinations can use this material.

An **average or more accurately an arithmetic mean** can be defines as the sum of n different data divided by n.

Averages of a group is defined as the ratio of sum of all the items in the group to the number of items in the group.

**Average = (Sum of all items in the group)/ Number of items in the group**

Now, sum of all items can be ‘the sum of number of quantities like apple, people etc’ or ‘sum of values of the item like 10 coins of 5 Rs each etc’.

**Find the Average Speed**

- If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by-
- If a person covers P km at x km/hr and Q km at y km/hr and R km at z km/hr, then the average speed in covering the whole distance is-
**{ (P+Q+R) / ( [P/x] + [Q/y] + [R/z] ) }**

**When a person leaves the group and another person joins the group in place of that person then-**

**If the average age is increased:**Age of new person = Age of separated person + (Increase in average × total number of persons)

**If the average age is decreased:**Age of new person = Age of separated person – (Decrease in average × total number of persons)

**When a person joins the group-**

**In case of increase in average:**Age of new member = Previous average + (Increase in average × Number of members including new member)

**In case of decrease in average**: Age of new member = Previous average – (Decrease in average × Number of members including new member)

**Average of n natural no’s**=(n+1)/2

**Average of even No**=(n+1)

**Average of odd No**= n

**General Formula**= (1st number +Last number)/2