# Averages Problems with Answers page 1

**1) What is the average of first 21 multiples of 7 ?**

**Answer:** 77

**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?**

**Answer:** 12.6 Yrs

**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**

**Answer:** 49

**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?**

**Answer:** 27

**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?**

**Answer:** 39

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