# Problems on Average: Basic concept, Questions and Solutions

Today I am going to tell you about **Average**. As we all know Average is an important topic in Quantitative Aptitude for competitive exams. As we all know Bank Po Exams, MBA Exams and other competitive exams has become very important so I request you before reading this article kindly subscribe to http://banking.eckovation.com/ and join the group. Our group code is

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**Basic Definition:-**

** **The word **‘Average’ **is used in everyday life to describe where the middle number of data set is. In statistics, the average is called the arithmetic mean. It is the typical number you would expect to find in series of numbers.

**Basic Concept:-**

1. Average = sum of observations/no. of observations

2. Suppose a boy covers a certain distance at x kmph and an equal distance at y kmph. Then the average speed during the whole journey is 2xy/x+y kmph.

**Examples:-**

1. Find the average of first 40 naturals numbers.

Solution- Sum of first n natural numbers = n(n+1)/2

so, sum of first 40 natural numbers = 40*41/2 = 820

Therefore Required Average = 820/40 = 20.5

2. A man bought 5 shirts at Rs 450 each, 4 trousers at Rs 750 each and 12 pairs of shoes at Rs 750 each. What is the average expenditure per article?

Solution- Total expenditure = Rs (5 * 450 + 4 * 750 + 12 * 750) = Rs (2250 + 3000 + 9000) = Rs 14250.

Number of articles = (5 + 4 + 12) = 21

Therefore Average expenditure = Rs (14250/21) = Rs 4740/7 = Rs 678.57

3. The average age of a man and his son is 40 years. The ratio of their ages is 11:5 respectively. What is the son’s age?

Solution- Let the ages of the man and his son be 11x and 5x years respectively.

Then, average age = (11x + 5x/2) years = 8x years

Hence son’s age = 5x = 25 years.

4. Of the three numbers, second is twice the first and is also thrice the third. If the average of three numbers is 44, what is the largest number?

Solution- Let the third number be x. Then, second number = 3x.

First number = 3x/2

Therefore x + 3x + 3x/2 = 44 * 3

that is 11x/2 = 132

x = 132 * 2/11 = 24

Hence largest number = 3x = 3 * 24 = 72.

5. The average of five numbers is 58. The average of first two numbers is 48.5 and the average of last two numbers is 53.5. What is the third number?

Solution- Third number = (Sum of 5 numbers) – (Sum of 4 numbers)

= (58 * 5) – [(48.5 * 2) + (53.5 * 2)]

= 290 – (97 + 107) = 290 – 204 = 86

# **Homework Questions:-**

Please refer to above examples and then try to solve these examples. If you are facing any difficulty then you can tell your doubts in the comment section.

1. Find the average of the following sets of scores: 385, 441, 876, 221, 536, 46, 291, 428

a. 221 b. 403 c. 428 d. 536 e. none of these

2. If 2a + 25b = 115, what is the average of a and b?

a. 2.5 b. 3.4 c. 4.5 d. 4.6

3. The average of 20 numbers is zero. Of them, at the most how many may be greater than zero?

a. 0 b. 1 c. 10 d. 19

4. The average of 2, 7, 6 and x is 5 and average of 18, 1, 6, x and y is 10. What is the value of y?

a. 5 b. 10 c. 20 d. 30

5. The average of odd numbers up to 100 is

a. 49 b. 49.5 c. 50 d. 50.5

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