# Average Questions & Formulas for Competitive Exams

To hold all the aces in competitive exams it is integral to master the Quantitative section encompassing everything related to Math basics from Mean Median Mode questions to Geometry questions. Apart from these, Average questions are also integrally covered under this aspect. Many bewildering problems are put under this topic, solving which the candidates often struggle. The concept of average in competitive exams is not the same as that covered in school, instead, it goes up to a higher level involving many intricacies. To ace this topic like a pro, here is a blog to help you with some advance average questions and formula.

## Concept of Average

Average can be basically determined as the equal distribution of a quantity in the same set of things. Mathematically, the average is the arithmetic mean of a set of quantity. It can easily be calculated by the following formula:

Let us understand this formula of average with a simple example:

Example: Find the average of these numbers 14, 34, 19, 20, 11?
Average= (11+14+19+20+34)/ 5
= 98/5 = 19.6

## Properties of Average

To get a better hold of the topic and to smoothly solve a variety of average questions, let us have a look at some of the properties of average:

• Average can also be referred to as Arithmetic Mean.
• Usually, the average is calculated for a set of numbers.
• The average must always lie above the lowest number and below the highest number.
• If the average of some numbers is A and N is added in each number, then the new average is (A + N).
• If the average of some numbers is A and N is subtracted from each number, then the new average is (A – N).
• For a set of numbers, is the average of the set is A, now all the numbers are multiplied by N, then the new average is (A x N).
• For a set of numbers, is the average of the set is A, now all the numbers are divided by N, then the new average is (A/N).

## List of Average Questions and Examples

We are familiar with the success mantra to crack the competitive exams, i.e., Practice, Practice and Practice. The more you gauge through the average questions, the stronger will be your grip over the topic. Before beginning with the advance level average questions, following are some solved examples:

Q. A building has only 3 rooms that contain 20, 30, and 10 chairs respectively. The percentage of broken chairs are 80%, 70% and 60% respectively then find the percentage of broken chairs in the entire building?

Solution:

Using the above-mentioned formula
The percentage of broken chairs= (20×80)+ (30×70)+ (10×60)/ (20+10+30)

= 4300/60
= 71.67%

Q. The average age of 30 male students in a school ids 10 years. If the teacher’s age is included, the average age becomes 11 years. What is teacher’s age?

Solution:

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Total age of 30 male students= 30×10=  300 years
The average age of 30 students and one teacher= 11 years
Total of their ages (including the teachers)= 31 x 11= 341 years
Teacher’s age= 341- 300= 41 years
Therefore, Teacher’s age=  41 years

Q. The average weight of 25 students is 30 kgs. If one of the students excluded, the average remaining students’ weight becomes 29 kgs.  What is the weight of excluded student?

Solution:

Total weight of 25 students= 25×30= 750 kgs
Average wwight of students without one student =  29 kgs

Total of their weight (excluding the student)= 24×29=  696 kgs
Weight of the excluded student= 750- 69
= 54 kgs

Check Out Our Exclusive Guide to Simple Interest Questions!

Here are some average questions for you to practice:

• The average marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and the failed candidates is 15, what is the number of candidates who passed the examination?
• A man bought 13 shirts of Rs 50 each, 15 pants of Rs 60 each and 12 pairs of shoes at Rs. 65 a pair. Find the average value of each article.
• The average of 11 results is 30, that of the first five is 25 and that of the last five 28. Find the value of the 6th number.
• A batsman in his 17th innings makes a score of 85, and thereby increase his average by 3. What is his average after 17th innings?
• In three numbers, the first is twice the second and thrice the third. If the average of these three numbers is 44, then the first number is?
• The production of a company for three successive years has increased by 10%, 20% and 40% respectively what is the average increase in production?

Other than the above-mentioned topics, you can also check out the following blogs covering the varied sections in competitive exams:

Hence, we hope that the above-elaborated basics and formulas and average questions will help you grab a better grip on the topic. If you are preparing for a competitive exam or are struggling between career choices, reach out to our experts at Leverage Edu and we will guide at every stage of your academic and professional journey thus ensuring that you take the right direction towards your dream career!