Average - Solved Questions and Answers

The average (or mean) is a single number that represents the central value of a set of numbers.

Formula:

Average = \frac {Number \ of \ values}{Sum \ of \ all \ values}

Average questions and answers are provided below for you to learn and practice.

Question 1: The average monthly salary of A and B is Rs. 7000. The average monthly salary of B and C is Rs. 8500, and the average monthly salary of A and C is Rs. 9000. What is the monthly salary of A?

Solution:

Let A, B, and C represent their respective monthly salaries. Then, we have:

A + B = (7000 × 2) = 14000 .... (i)

B + C = (8500 × 2) = 17000 .... (ii)

A + C = (9000 × 2) = 18000 .... (iii)

Adding (i), (ii), and (iii), we get: 2(A + B + C) = 49000 or A + B + C = 24500 .... (iv)

Subtracting (ii) from (iv)

A + B + C = 24500 .... (iv) and B + C = 17000 .... (ii)

we get A = 7500.

A's monthly salary = Rs. 7500.

Question 2: The average age of a father, mother, and their daughter 4 years ago was 30 years, and that of the mother and daughter 6 years ago was 25 years. What is the present age of the father?

Solution:

Let the present ages of the father, mother, and daughter be F, M, and D, respectively.

The average age of the father, mother, and daughter 4 years ago was 30 years:

(F − 4) + (M − 4) + (D − 4)/3​ = 30

Simplifying, we get:

F + M + D − 12 = 90  ⟹  F + M + D = 102 ... (i)

The average age of the mother and daughter 6 years ago was 25 years:

(M − 6) + (D − 6)/2 = 25

Simplifying, we get:

M + D − 12 = 50 ⟹ M + D = 62 ... (ii)

Now, we can substitute equation (ii) into equation (i):

F + (M + D) = 102  ⟹  F + 62 = 102

Solving for F:

F = 102 − 62 = 40

Thus, the present age of the father is 40 years.

Question 3: In the first 12 overs of a cricket match, the run rate was 5.5. What should be the run rate in the remaining 38 overs to reach the target of 300 runs?

Solution:

Calculate runs scored in the first 12 overs:

Runs scored = Run rate × Overs = 5.5 × 12 = 66 runs

Calculate runs still needed:

Runs needed = Target − Runs scored = 300 − 66 = 234 runs

Calculate the required run rate in the remaining 38 overs:

Required run rate = Runs needed/Remaining overs

= 234/38 ≈ 6.16

Since we need a whole number, we can round this up to 7 runs per over.

To reach the target of 300 runs, the required run rate in the remaining 38 overs is approximately 7 runs per over.

Question 4: A baker has sales of Rs. 7800, Rs. 8200, Rs. 7900, Rs. 8600, and Rs. 8100 for 5 consecutive months. How much sale must he have in the sixth month to achieve an average sale of Rs. 8000?

Solution:

Calculate the total sales needed for 6 months to achieve an average of Rs. 8000:

Total sales needed = Average sale × Number of months = 8000 × 6 = 48000.

Calculate the total sales for the first 5 months:

Total sale for 5 months = Rs. (7800 + 8200 + 7900 + 8600 + 8100) = Rs. 40600.

Required sale = Rs. (48000 - 40600)

= Rs. 7400.

The baker must have a sale of Rs. 7400 in the sixth month to achieve an average sale of Rs. 8000 over six months.

Question 5: A student's score was incorrectly recorded as 75 instead of 65. Because of this error, the class average increased by 0.4 marks. What is the total number of students in the class?

Solution:

• Let n be the number of pupils in the class.
• Let S be the original total marks of the class.

New total score:
S + (75 − 65) = S + 10

New average:
S + 10/n

Original average:
S/n​

Equation based on the increase in average:
S + 10/n = S/n + 0.4

Multiply by n:
S + 10 = S + 0.4n

Simplify:
10 = 0.4n

Solve for n:
n = 10/0.4 = 25

Conclusion:

The total number of students in the class is 25.

Question 6: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

Solution:

Let the average age of the whole team be x.

Total age of the team = 11x

The total age of the captain and wicket keeper is:26 + 29 = 55

Total Age of Remaining Players =11x − 55

Average Age of Remaining Players = (11x − 55)/9

According to the problem, this average is one year less than the average age of the whole team:

(11x − 55)/9 = x − 1

11x − 9x = 55 − 9

2x = 46

​x = 23

The average age of the team is 23 years.

Question 7: A grocery store purchases flour at Rs. 12, Rs. 15, and Rs. 18 per kilogram in three consecutive months. If the store spends Rs. 6000 each month, what is the average cost per kilogram of flour after the three months?

Solution:

Total quantity of flour consumed in 3 months:

Quantity = (6000/12 + 6000/15 + 6000/18)

Total Quantity = 500 + 400 + 333.33 ≈ 1233.33 kg

Total Amount = 6000 × 3 = 18000 Rs.

Average Cost = Total Quantity/Total Amount​ = 18000​/1233.33 ≈ 14.59 Rs.

The average cost per kilogram of flour after the three months is approximately Rs. 14.59.

Question 8: If the average score of four groups of 30, 40, 35, and 50 students is 70, 75, 80, and 65 respectively, what is the overall average score of all the students combined?

Solution:

Required Average = (30 × 70) + (40 × 75) + (35 × 80) + (50 × 65)​/30 + 40 + 35 + 50

Total Scores=2100 + 3000 + 2800 + 3250 = 11150

Total Students = 30 + 40 + 35 + 50 = 155

Overall Average = 11150/155 ​≈ 71.94