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Average involving time, speed and distance

2456.png
 
However, while solving the questions involving time, speed and distance, we should assume some distance, preferably the LCM of all the given speeds.
 
Example
Lovely goes to Patna from New Delhi at a speed of 40 km/h and returns with a speed of 60 km/h. What is her average speed during the whole journey?
Solution
Assuming that the total distance between Patna and New Delhi is 120 km (LCM of 40 and 60) the total time taken (Patna − New Delhi and New Delhi − Patna) = 3 + 2 = 5 h
So, Average speed = 2465.png = 48 km/h
 

Average involving age

Average of a group of n persons given at any point of time can be calculated in the following way
 
3386.png
 
Example
The average age of the 5 members of a family is 20 years. The youngest member of the family is 4 years old. At the time of his birth the average age of the rest of the family was N years. What is the average age of the family (in terms of N) excluding the youngest member?
Solution
Sum of ages of all the members of the family = 100
 
Sum of ages of all the members of the family excluding the youngest number = 100 − 4 = 96
 
So, average age of all the members of the family excluding the youngest number = 96/4 = 24 = N
 
What is the average age of the family(in terms of N) excluding the youngest member = N + 4
 

Average involving number system

  1. Average of 1st n consecutive natural numbers 2504.png
     
    For example, the average of 1st five natural numbers = 3
  2. The average of 1st n consecutive even natural numbers = n + 1
     
    Sum of 1st n consecutive even natural numbers n(n + 1)
     
    For example, the average of 1st five even natural numbers = 6
  3. The average of 1st n consecutive odd natural numbers = n
     
    Sum of 1st n consecutive odd natural numbers = n2
     
    For example, the average of 1st five odd natural numbers = 5




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