FeedBack Form

Your Name :
Your Email :
Your Location :
Your Message :
   
FeedBack

Average Problems

Aptitude

AVERAGE -> IMPORTANT FACTS AND FORMULAE

I. Average = [Sum of observations / Number of observations]
II. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is [2xy / x + y] kmph.

AVERAGE -> SOLVED EXAMPLES

1. Find the average of all prime numbers between 30 and 50.
  Sol. There are five prime numbers between 30 and 50.
They are 31, 37, 41, 43 and 47.
∴ Required average = [(31 + 37 + 41 + 43 + 47) / 5] = 199/5 = 39.8.
2. Find the average of first 40 natural numbers.
  Sol. Sum of first n natural numbers = 40 * 41 / 2 = 820.
∴ Required average = 820 / 40 = 20.5.
3. Find the average of first 20 multiples of 7.
  Sol. Required average = 7(1+2+3 ... + 20) / 20 = [7 * 20 * 21 / 20 * 2] = [147 / 2] = 73.5.
4. The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53kg is replaced by a new man. find the weight of the new man.
  Sol. Total weight increased = (1.8 * 10)kg = 18kg.
∴ Weight of the new man = (53 + 18)kg = 71kg.
5. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. find his average after 17th inning.
  Sol. Let the average after 17th inning = x.
Then, average after 16th inning = (x - 3)
∴ 16(x - 3) + 87 = 17x or x = (87 - 48) = 39.

Average -> EXERCISE

34. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
 
  • A. 23 years
  • B. 24 years
  • C. 25 years
  • D. 27 years
Ans: A.
Sol.
Let the average age of the x whole team be x years.
∴ 11x - (26 + 29) = 9( x - 1 )
⇒ 11x - 9x = 46
⇒ 2x = 46
⇒ x = 23.
So, average age of the team is 23 years.
 
35. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
 
  • A. 35 years
  • B. 40 years
  • C. 50 years
  • D. 60 years
Ans: B.
Sol.
Sum of the present ages of husband, wife and child
= (27x3+3x3) years = 90 years.
Sum of the present ages of wife and the child
= (20 x 2 + 5 x 2) years = 50 years.
∴ Husband's present age = (90 - 50) = 40 years.
 
 
36. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
 
  • A. 53.33
  • B. 54.68
  • C. 55
  • D. 57
Ans: B.
Sol.
Required average = [55x50 + 60x55 + 45x60 / 55 + 60 + 45]
= [2750 + 3300 + 2700 / 160]
= 8750 / 160 = 54.68.