How to solve mathematical operations in reasoning? Tips and Tricks

Do you know what is the common feature in the Reasoning section of every competitive exam? Actually most of the competitive exams include a greater number of questions from the topic “Mathematical Operations” that comes in Verbal Reasoning chapter. Take example of SSC, RBI, Railway or IBPS CLERK/PO or CSAT/CAT/MAT, this topic is considered to be quiet important and every year 2-3 number of puzzles are asked from this topic and you know well two or three questions are enough to decide who is going to qualify the exam or who are not going to.  We will explain today tips and tricks of different types of questions that were asked in previous years in different exams from the mathematical operators topic. I am sure it will help you in the upcoming SSC Exams. You can download some practice questions in PDF format from the bottom of the article.


We will deal first questions on simple mathematical operations. In this article we will mention four fundamental operations —

i) addition ii) subtraction iii) multiplication and iv) division.

We will also talk how to solve those statements kind of questions — such as less than\ ‘greater than’, ‘equal to’, ‘not equal to, etc. are represented by symbols, different from the usual ones.

First you should know what different kinds of questions are asked from this topic.

As far as I know you will be given four kinds of questions from this topic.

  • Substitute the symbols
  • Balance the Equation
  • Swapping of Signs and Numbers
  • Mad Mathematical Operations based on several different patterns

Before starting this most interesting topic, you should master first the BODMAS Rule that is Brackets, Of, Division, Multiplication, Addition, Subtraction

B Brackets first (parentheses)

O Of (orders i.e. Powers and Square Roots, Cube Roots, etc.)

DM Division and Multiplication (start from left to right)

AS Addition and Subtraction (start from left to right)

Example of BODMAS rule: 

Example: How do you work out 12 / 6 × 3 / 2 ?

Multiplication and Division rank equally, so just go left to right:

First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3


Now we will move to those four topics that mentioned above:-

#1 Substitute the symbols

In this type of question, you will be provided substitutes for various mathematical symbols, followed by a question that will include calculation of an expression or you will have to choose which equation is right or wrong. You will be aksed to put the real signs in equation and solve the question accordingly.

If × stands for ‘addition’, ÷ stands for ‘subtraction’, + stands for ‘multiplication’ and-stands for ‘division’, then 20 × 8 ÷ 8 – 4 + 2 = ?

A) 80 B) 25
C) 24 D) 5

Answer: C) 24


By the Given data , We have the expression:

20 + 8 – 8 ÷ 4 × 2 = 20 + 8 – 2 × 2 = 20 + 8 – 4 = 24.


#2 Balance the Equation

In this type of questions, you will given an equation without any sign. You will have to fill those gaps between the numbers with arithmetic signs given in the options to make the whole equation right.

You must correctly place signs in this problem to create a correct solution.

For example:-

Ex : If the following equations has to be balance, then the signs of which of the following options will be used?

24 6  12  16 = 0

(a) – , + and +

(b) ÷, + and ÷

(c) -, – and –

(d) ÷, + and –

Solution: (d)

From Option (a)


Like above options we have to check one by one.

From Option (d)


Hence, option (d) is correct.

#3 Swapping of Signs and Numbers

In this type of questions, you are given an equation and you have to find out which option’s solution is correct.  But buddy it is not easy. You will see all options’ solutions are wrong. That is why you will have to interchange the signs or numbers from the given alternatives and then you will have if after interchanging the signs/numbers the pairs given in options become right.

Ex: Which one of the given interchange in signs would make the given equation correct?

A) 4 + 8 – 12 = 12 B) 4 – 8 + 12 = 0
C) 8 + 4 – 12 = 24 D) 8 – 4 + 12 = 8


Answer:   B) 4 – 8 + 12 = 0


 On interchanging + and – and 4 and 8 in (b),

we get the equation as

8 + 4 – 12 = 0
or 12 – 12 = 0
or 0 = 0, which is true.

See another example:–

Find out the two signs to be interchanged for making following equation correct :
5 + 3 x 8 – 12 ÷ 4 = 3


A. + and –
B. – and ÷
C. + and x
D. + and ÷
Answer: (Solve yourself)

# 4 Mad Mathematical Operations based on several different patterns

This is totally a mad type of questions that are not based on logic. Here you have to find out solution of a particular equation seeing the pattern of the given equations in question. Here you don’t have to play with arithmetic signs or you do not have to use your mathematical brain. Just see the example given below.


Ex: If 9 ×5×2 = 529 and 4 ×7×2 =724, then 3×9×8 =?

(a) 983

(b) 839

(c) 938

(d) 893

Solution: (a)





Download PDF to practice some puzzles/questions of mathematical operations.

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