# Basic concepts & Tricks to solve Average Problems

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## 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