WORD PROBLEMS ON AVERAGE

The formula given below can be used to find average of the given values.

Problem 1 :

Chicago can get a lot of rain in the rainy season. The rainfall during a period of 6 days was 90 mm, 74 mm, 112 mm, 30 mm, 100 mm and 44 mm. Find the average daily rainfall during this period.

Solution :

Average daily rainfall :

= 75 mm per day

Problem 2 :

Compare the average of the three even whole numbers from 2 to 6 and the average of the four odd whole numbers from 1 to 7.

Solution :

Three even whole numbers from 2 to 6 : 

2, 4, 6

Average of three even whole numbers from 2 to 6 :

= 4 ----(1)

Four odd whole numbers from 1 to 7

1, 3, 5, 7

Average of four odd whole numbers from 1 to 7 :

= 4 ----(2)

Comparing (1) and (2), 

4 = 4

Average of the three even whole numbers from 2 to 6 and the average of the four odd whole numbers from 1 to 7 are equal.

Problem 3 :

Chicago can get a lot of rain in the rainy season. The rainfall during a period of 6 days was 90 mm, 74 mm, 112 mm, 30 mm, 100 mm and 44 mm. Find the average daily rainfall during this period.

Solution :

Average daily rainfall :

= 75 mm per day

Problem 4 :

A dog  slept 6 hours on Sunday, 8 hours on Monday and 420 minutes on Tuesday. Find the average number of hours the dog slept per day.

Solution :

Sunday ----> 6 hrs

Monday ----> 8 hrs

Tuesday ----> 420 min = ⁴²⁰⁄₆₀ hrs = 7 hrs

Average number of hours the dog slept per day :

= 7

Problem 5 :

Mr. Lenin finds the average of the following numbers.

3, 8, 19, 17, 21, 14, k

If the average found by him is 12, find the value of k.

Solution :

Given : Average of 3, 8, 19, 17, 21, 14 and k is 12.

Multiply both sides by 12.

82 + k = 84

Subtract 82 from both sides.

k = 2

Problem 6 :

Find the average of all prime numbers between 30 and 50.

Solution :

The prime numbers between 30 and 502 are

31, 37, 41, 43, 47

Average of all prime numbers between 30 and 50 :

= 39.8

Problem 7 :

Find the average of first 50 natural numbers.

Solution :

Formula to find the sum of first n natural numbers :

ⁿ⁽ⁿ ⁺ ¹⁾⁄₂

Substitute 50.

⁵⁰⁽⁵⁰ ⁺ ¹⁾⁄₂

= 25(51)

= 1275

Sum of first 50 natural numbers is 1275.

Average of first 50 natural numbers :

= 25.5

Problem 8 :

If the average of four consecutive integers is 12.5, find the integers.

Solution :

Let x be the first integer.

Then the four consecutive integers are

x, (x + 1), (x + 2), (x + 3)

Given : Average of four consecutive integers is 12.5.

Average = 12.5

Multiply both sides by 2.

2x + 3 = 25

Subtract 3 from both sides.

2x = 22

Divide both sides by 2.

x = 11

x + 1 = 12

x + 2 = 13

x + 3 = 14

Therefore, the four consecutive integers are

11, 12, 13, 14

Problem 9 :

If the average of four consecutive odd integers is 10, find the largest of these integers.

Solution :

Let x be the first odd integer.

Then the four consecutive odd integers are

x, (x + 2), (x + 4), (x + 6)

Given : Average of four consecutive odd integers is 10.

Average = 10

x + 3 = 10

Subtract 3 from both sides.

x = 7

The largest integer :

= x + 6

= 7 + 6

= 13

Problem 10 :

John played 4 games of badminton and scored an average of 12 points per game. The average score of the first 3 games was 10 points per game. Find the points scored by John in the 4th game.

Solution :

Average of 4 games = 12

sum of the points in 4 games = 48 ----(1)

Average of first 3 games = 10

sum of the points in first 3 games = 30 ----(1)

Points scored by John in the 4th game :

= (2) - (1)

= 48 - 30

= 18

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