Solved Questions and Answers for Average

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 x 41 / 2
                                    = 820.
=> Required average = 820 / 40
                    = 20.5.

3. 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.

4. The average age of boys in the class is twice the number of girls in the class. If the ratio of boys and girls in the class of 36 be 5 : 1, what is the total of the ages (in years) of the boys in the class.
Sol: Number of boys = 136 x (5/2)
                                 = 30,
Number of girls 6.
Average age of boys = (2 x 6)
                                = 12 years.
Total age of boys (30 x 12) years = 360 years.

5. The average of four consecutive even numbers is 27. The largest of these numbers is
Sol: Let the numbers are x, x+2, x+4 and x+6. Then,
  (x+x+2+x+4+x+6)/4 = 27
=> 4x+ 12/4 = 27
=> x + 3 = 27
=> x = 24
Largest number = (x + 6) = 24 + 6 = 30.