Average II- Different kinds of Average Problems to Calculate Average

Different kind of Average Problems are asked in SBI PO, IBPS, SSC CGL and all other competitive exams which need you to calculate average or changes in average. Read on to find out smart methods to calculate average.

A frequently asked topic in SBI PO, IBPS and SSC Exams, average problems can be both- simple and complex in nature. Though most problems where you have to calculate average can be solved by using the average formula, average problems of a higher degree may need some additional skills and techniques. After discussing what is average and the average formula in the previous blog, let’s move to the next blog in the series, where we will discuss the kind of average problems asked in competitive exams.
Average problems can be divided into two categories- one where you used the basic average formula to calculate average and ones where you have to use the concept of weighted average to calculate average.

Set I – Basic Average Problems Using the Average Formula

We know that Average is nothing but the equal distribution of the given amount among the elements of a group. So in this section we will discuss average problems that can be solved by the use of the average formula.

Problem 1: Kamlesh bought 65 books from one shop for Rs.1050/- and 50 books for Rs.1020/- from another shop. What is the average price he paid per book?

Solution 1:
We know the formula to calculate average -
Step 1
We know that Kamlesh has bought 65 and 50 books from two shops for Rs.1050 and Rs.1020 respectively. So we can substitute these values in the average formula to calculate average price per book.

Substituting values we get,
Average Price per Book = ( 1050 + 1020 ) / ( 65 + 50 )
Average Price per Book = 2070 / 115
Average Price per Book = 18

Therefore the average cost of one book is Rs.18

Problem 2: Average of 5 positive integers is 436. The average of first two numbers is 344 and the average of last two numbers is 554. What is the third number?

Solution 2:
We know the average formula that is used for calculating the sum-
Using this average formula we can solve problems on average involving sum. Now in this problem there are five elements and their average is mentioned. We have been given the average of the first two and the last two values and have to find out the third value.

Step 1
Assuming the 5 numbers to be a, b, c, d and e, we get the equation –
a + b + c + d + e = 436 x 5
a + b + c + d + e = 2180      (i)

Step 2
We know that the average of first two numbers is 344 and the last two numbers is 554. Therefore we can say –
a + b = 344 x 2      (ii)
d + e = 554 x 2      (iii)

Step 3
Substituting values from equations (ii) and (iii) in equation (i), we get-
(344x2) + c + (554x2) = 2180
688 + c + 1108 = 2180
c + 1796 = 2180
c = 384
Therefore the value of the 3rd number is 384.

Once you master the concept of average, the smart way to smart average problems like this will be to eliminate the step involving equations (ii) and (iii) and directly put the values in equation (i) to solve the problem in less time.

Set II – Weighted Average Problems Using the Advanced Average Formula

Before we move ahead to discuss average problems of this kind let us discuss what is combined average or weighted average. If the average of a group of n1 elements is a1, and the average of another group of n2 elements is a2 and so on, then the average of all the groups taken together will be-
Therefore this average formula is extremely helpful when two different groups are given to us and we have to calculate average for the groups.
Let’s presume a group a group n1 where the average age of the group is a1 and another group n2 where the average age is a2.
So the sum of elements in G1 and G2 can be written as –
And the combined average of both the groups together can be written as -
Problem 1: In a class there are 32 boys and 28 girls, if the average age of the boys is 14 years and the average age of the girls is 13 years, calculate average age of the whole class.

Solution 1:
In this question, we have two groups of elements, the boys and the girls. The average age of 32 boys is 14 and average age of 28 girls is 13. We can use the combined average formula to calculate average of the whole class-
Step 1
The average age of the class will be the combined average of the class. We can substitute the values in the formula and get our answer –
Average Age of the Class = [(32 x 14) + (28 x 13)] / (32 + 28)
Average Age of the Class = 812 / 60
Average Age of the Class = 13.53

The average age of the whole class will be 13.53