Average Questions Basic with Solution

Solution:

Prime numbers before 32 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. ⇒ Sum of prime numbers = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 +  31

⇒ Sum of prime numbers = 160 

⇒ Count of prime numbers = 11 

⇒ Average = Sum of prime numbers / Count of prime numbers

⇒ Average = 160 / 11 

⇒ Average ≈ 14.54 

∴ The correct answer is option 1.

Solution:

Average of four given consecutive odd nubmers = (x1 + x2 + x3 + x4)/4 Average of three given consecutive even numbers = (y1 + y2 + y3)/3 (x1 + x2 + x3 + x4)/4 = (y1 + y2 + y3)/3 – 6 

→ (x1 + x2 + x3 + x4)/4 = 34

Solution:

Let the age of teachers be y. 

And the age of Student be x. 

Difference y = (x + 20) 

According to the question: 

Average age = (x + x + x + y)/4 = 25 years 

(3x + y) = 25 × 4 → 3x + x + 20 = 100 → The age of teachers, y = (x + 20)  = 20 + 20 = 40 years  

Solution:

Sum of numbers = 642 + 253 + 834 + 303 → 2032 

Average = 2032 / 4 → 508

Solution:

Sum of prime numbers = 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 Sum = 474 → Count of prime numbers = 8 

Average = Sum / Count 

Average = 474 / 8 → 59.25

Solution:

The total weight of P and his three friends = 55 × 4 = 220 kg Let, the average weight of three friends = x 

So, the total weight of three friends = 3x

The weight of P = x + 4 

Then, (x + 4) + 3x = 220 

x = 216/4 = 54 

∴ P's weight = 4 + 54 = 58 kg

Let age of P, Q, R and S be P, Q, R and S respectively. 

P + Q + R = 24 × 3 → P + Q + R = 72→ P + Q + R + S = 30 × 4 = 120 The age of S is 48 years. → Total age of five persons = 172 Average age of 5 persons = 172/5 = 34.4 years

Solution:

The batting average for 27 innings of a cricket player is 47 runs. The batting average for 25 innings is 42 runs (High and Low score excluded) 

Here, Average decreases by (47 - 42) = 5 

So, Total runs in that two innings (H + L) = 47 + 47 + (25 × 5) = 219 runs Difference of runs in that two innings (H - L) = 157 runs 

So, 2H = 219 + 157 

H = 376/2 = 188 runs

Solution:

Average of 28 numbers = 77 

Average of first 14 numbers = 74 

Average of last 15 numbers = 84 

Deviation on first 14 numbers = 74 - 77 = - 3 × 14 = - 42 

Deviation on last 15 numbers = 84 - 77 = 7 × 15 = 105 

14th number = 77 - 42 + 105 = 140 

∴ Average of remaining 27 numbers = (28 × 77 - 140) ÷ 27 = 74.7

Solution:

The sum of nine numbers = 60 × 9 = 540 

The sum of the first five numbers = 55 × 5 = 275 

The sum of the next three numbers = 65 × 3 = 195 

Ninth number = (540 – 275 – 195) = (540 – 470) = 70 

∴ Tenth number = 70 + 10 = 80

Solution:

Difference between wrong and actual numbers = 91 – 46 = 45 As the actual number is less than the wrong number  

So the average decreased by 45/45 = 1  

The correct average = 150 – 1 = 149 

∴ The correct average is 149 

Solution:

Average of numbers = Sum of numbers / Total numbers 

Average of first 12 numbers is 15 

Sum of 12 numbers = 15 × 12 = 180 

New number 41 is to be added 

Average of 13 numbers = (Sum of 12 numbers + 13th number)/13 Average = (180 + 41) / 13 = 221 / 13 = 17 

Solution:

New average = Old average + (Change in number / Total numbers) New average of 40 numbers = 71 + (140 – 100)/40 = 71 + 1 = 72 ∴ The average increased = 72 – 71 = 1 

Solution:

The average age of three boys = 22 

Total Age of three boys = 66 years 

Let the ages of three boys be 6a, 9a, and 7a respectively. 

6a + 9a + 7a = 66 

a = 3 

Age of youngest boy = 18 years.

Solution:

The sum of all the observations here is 87 + 84 + 86 + 90 +82 + 88 +78 =  595 

Number of observations = 7 

So, Average = 595/7 = 85

Solution:

Average of 4 terms = 20 

Hence, the total sum of 4 terms = 80 

Let terms be A, B, C, D 

So, the sum will be A + B + C + D =80 

Given, 3A = B+C+D 

So, 4A = 80, 

A = 20

Solution:

Average of A, B, C is 25 

So, sum of their ages  = 75 

Now, the sum of B and C will be 50 (because their average is 25) So age of A = 75 - 50 = 25 years

Solution:

The average of 7 consecutive numbers is n implies that the 4th term is equal to n. 

Now if we include next two terms then the average of 9 terms will be the 5th  term. Now as the terms are consecutive, so the 5th term will be n + 1.

Solution:

Total score for 9 innings is 75 × 9 = 675 

Total score after 10th innings = 675 + 100 = 775 

So, average = 775 / 10 = 77.5