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.
