###
**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 3

^{rd}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 n

_{1}elements is a_{1}, and the average of another group of n_{2}elements is a_{2 }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 n

_{1}where the average age of the group is a_{1 }and another group n_{2}where the average age is a_{2.}
So the sum
of elements in G

_{1}and G_{2 }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

###
**Average Problems for Practice **

Try these average
problems on leave your answers in the comments section below-

Question 1:
In a certain school, there are 60 boys of age 12 each, 40 of age 13 each, 50 of
age 14 each and 50 of age 15 each. What is the average age of all the boys of
the school?

1) 13.50 2) 133.1 3) 13.45 4) 14 5) None of these

Question 2:
The average age of 20 students of a section is 12 years. The average age of 25
students of another section is 12 years. What is the average age of both the
sections combined together?

1) 11 2) 11.5 3) 11.75 4) Cannot be determined 5) None of these

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