Dear Aspirants, Here we have given the General Rules to Solve Average and Percentage Problems in PDF. Candidates those who are applied for the Competitive examinations can use this material.ย

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**General Rules to Solveย Average and Percentageย Problems-Download**

__1. General Rules we must know to solve Averages Problems__

**Formula:**

- Average: = (Sum of observations / Number of observations).

**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 A km at x km/hr and B km at y km/hr and C km at z km/hr, then the average speed in covering the whole distance is-ย { (A+B+C) / ( [A/x] + [B/y] + [C/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 ร total number of persons)**If the average age is decreased,**= Age of separated person โ (Decrease in average ร total number of persons)

Age of new person

**When a person joins the group-**

**In case of increase in average**

Age of new member = Previous average + (Increase in average ร Number of members including new member)

**In case of decrease in averageย ย ย :**Age of new member = Previous average โ (Decrease in average ร Number of members including new member)

__2. General Rules we must know to solve Percentages__

__2. General Rules we must know to solve Percentages__

**Basic Rules:**

- If the price of the commodity increases by R%, then the reduction in the consumption as not to increase the expenditure is [R/(100+R)x100]%.
- If the price of the commodity decreases by R%, then the increase in the consumption as not to increase the expenditure is [R/(100-R)x100]%.
- If A is R% more than B, then B is less than A by [R/(100+R)x100]%.
- If A is R% less than B, then B is less than A by [R/(100-R)x100]%.

**Rules for Population Problems:**

Let the population of a town be P now and suppose it increases at the rate of R% per annum then:

- Population after n years = P(1+R/100)
^{n} - Population n years ago = P/(1+R/100)
^{n}

**Rules for Depreciation Problems:**

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum then

- Value of the machine after n years = P(1-R/100)
^{n} - Value of the machine after n years = P/(1-R/100)
^{n}

**Things to be remembered:**

**1 = 100%****1/2 = 50%****1/3 = 33 %****1/4 = 25%****1/5 = 20%****1/6 = 16 %****1/7 = 14 %****1/8 = 12 %****1/9 = 11 %****1/10 = 10%****1/11 = 9 %****1/12 = 8 %****1/13 = 7 %**

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