# Averages Problems with Answers page 1

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1) What is the average of first 21 multiples of 7 ?
Explanation:
Required average = 7(1+2+….+21) / 21
(7/21)X ( (21×22) / 2 ) (because sum of first 21 natural numbers)
= 77

2) In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Explanation:
Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years

3) The average age of a class of 32 students is 16 yrs. if the teacher’s age is also included, the average increases by one year. Find the age of the teacher
Explanation:
Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher’s age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher’s age is 16+(33X1) = 49 Years

4) The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Explanation:
The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 – 99 ) = 27

5) Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?