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Averages

Part 1: Introduction - 1

Concept 1: 

Basic Models:

In this, the candidate will learn about the all basic problems in Averages. Entire averages topic is depends on one standard formulae i.e; 

Average = Sum of Obs. / No. of Obs.

Along with the above formulae, the candidate must learn some more additional formulae in order to solve the problems in Averages.

Important Formulae:

1. The average of first ‘n’ consecutive odd numbers is ‘n’.

2. The average of first ‘n’ consecutive even numbers is ‘n+1’.

3. Average of odd numbers from 1 to n is 

Average = (Last odd number + 1) / 2

4. Average of even numbers from 1 to n is 

Average = (Last even number + 2) / 2

5. If the difference between any two consecutive numbers is same, then

Average = (First number + Last number) / 2

6. The average of ‘n’ numbers is A.

a) if each number is multiplied by ‘k’, then new average = A × k

b) if each number is added by ‘k’, then new average = A + k

c) if each number is subtracted by ‘k’, then new average = A – k

d) if each number is divided by ‘k’, then new average = A ÷ k

Eg: Find the average of 35, 43, 45, 48, 56, 67, 70.

Sol: Average =  Sum of Obs. / No. of Obs.

Average = (35 + 43 + 45 + 48 + 56 + 67 + 70) / 7 = 364 / 7 = 52.

Concept 2: 

Weighted Average Problems:

Eg: There are 40 boys and 50 girls in a class. If the average weight of boys is 54 kg and the average weight of girls is 45 kg. What is the average weight of entire class?

Sol: Average weight of entire class = (Sum of boys + Sum of girls) / Total Strength 

Sum of boys = Average of boys × No. of boys = 54 × 40 = 2160 kg

Sum of girls = Average of girls × No. of girls = 45 × 50 = 2250 kg           Average weight of entire class = (2160 + 2250) / (40 + 50) = 49 kg.

Concept 3:

Average Speed:

In general, average speed depends on two conditions.

1) Distances are equal 2) Distances are not equal

1) Distances are equal: 

If there are two equal distances, then the 

Average Speed = 2S1S2 / (S1 + S2)

If there are three equal distances, then the

Average Speed = 3S1S2S3 / (S1S2 + S2S3 + S3S1)

2) Distances are not equal:

If distances are not equal, then the

Average Speed = Total Distance / Total Time

Eg: A boy is going to school from his house at a speed of 30 kmph and return home at a speed of 45 kmph. Find the average speed.

Sol: In the given problem, distances are equal in both the cases.

Average speed = 2S1S2 / (S1 + S2)

             ⸫ Average speed = 2 × 30 × 45 / (30 + 45) = 36 kmph.

Eg: A man covers three equal distances at a speeds of 15 kmph, 20 kmph and 30 kmph respectively, then find the average speed during the entire journey.

Sol: According to question, man covers 3 equal distances. 

Then, Average speed = 3S1S2S3 / (S1S2 + S2S3 + S3S1) 

⸫ Average speed = 3 × 15 × 20 × 30 / (15 × 20 + 20 × 30 + 30 × 15) = 20 kmph.

Eg: An aeroplane travels distances 1200 km, 1500 km and 2000 km with a speeds of 600 kmph, 500 kmph and 400 kmph respectively. What is the average speed of entire journey?

Course Feature

  • Category Aptitude
  • Course Duration 4hr 18mins
  • Language English
  • Price Free
  • Validity Life Time
  • Rating 4 | 9 Reviews
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