Arithmetical Reasoning and Figural Classification for SSC and Railways Exams

By : Neha Uppal

Updated : Nov 19, 2020, 17:11

Arithmetical reasoning and figural classification questions are asked in almost every SSC and Railway related competitive exams - be it SSC CGL, SSC CHSL, SSC JE, HSSC Patwari, HSSC Canal Patwari, HSSC Sachiv, HSSC Clerk, Delhi Police, RRB Group D, RRB JE, RRB NTPC, RRB ALP, SSC MTS, SSC CPO, SSC Steno, SSC Constable or any other related competition in government sector in India.

Arithmetical reasoning consists of a numeral or a word problem to be solved using basic arithmetic. These questions encircle a variety of concepts to solve using basic mathematics like ages and weights, number system, ratio and proportion, profit, loss and discounts, time and distance, sequences and patterns, fractions and percentages, time and work, simple and compound interest, HCF and LCM, pipes and cisterns, games and tournaments, probability, square roots etc.

Figural classification questions are the means to judge a candidate’s non-verbal capabilities, keen observance and general intelligence quotient. In such types of questions, mainly a group of figures except one belongs to a particular pattern, whereas the ignored one is the odd one out not resembling that pattern and the candidate has to identify this odd patterned option. As an example, to one such figural classification question

byjusexamprepIn figure (c) only, two out of the four elements are opening in the same direction. Hence the answer would be (c). Figural questions practice may come handy in the data interpretation section also.

Important arithmetical reasoning and figural topics



Natural numbers

Counting numbers 1, 2, 3, 4, 5, ... are called natural numbers

Whole numbers

All counting numbers together with zero form the set of whole numbers. Thus, (i) 0 is the only whole number which is not a natural number. (ii) Every natural number is a whole number.

Even numbers

A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8, 10, etc.

Odd numbers

A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7, 9, 11, etc

Prime numbers

A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.

Composite numbers

Numbers greater than 1 which are not prime, are known as

composite numbers, e.g., 4, 6, 8, 9, 10, 12.


Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes

Distributive law

(i) a * (b + c) = a * b + a * c, and (ii) a * (b-c) = a * b - a * c

Euclidean algorithm

If we divide a given number by another number, then:

Dividend = (Divisor x Quotient) + Remainder

Basic and important formulae


Arithmetic progression

If every upcoming term of a progression differs from its previous term by a constant value, then it is called an AP.

Geometrical progression

A GP is where every term holds a constant ratio with its previous term

Highest Common Factor

The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly

Least Common Multiple

The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

Laws of Indices, and Law of Surds



The ratio of two quantities a and b in the same units is the fraction a/b and we write it as a:b


The equality of two ratios is called proportion.

If a: b = c: d, we write, a: b:: c : d and we say that a, b, c, d are in proportion

Direct proportion

Two quantities are said to be directly proportional if on the increase (or decrease) of the one, the other increases (or decreases) to the same

Inverse proportion

Two quantities are said to be inversely proportional if on the increase of the one, the other decreases to the same extent and vice-versa.

Time and distance

Speed=distance/time, Time=distance/speed, and distance=time*speed.

Tips to solve/prepare arithmetical reasoning and figural classification questions

  • The most important tip for solving the arithmetical reasoning and figural classification questions is Time Management, and that comes from one thing only- Practice. Practice as many questions as you can. Keep a time track too.
  • Go on solving the numerical problems, rather than mugging the theory.
  • Learn short-cut methods, but do not jump the steps for solving arithmetical reasoning questions.
  • Keep the thumb-rules handy. This will help to lower the attempt time and ensure the answer's accuracy.

Importance of arithmetical reasoning and figural classification in SSC and Railway exams

  • If to analyse SSC-CGL previous three years papers, an average of 48% (12 out of 25) of questions in Quantitative Aptitude section which carries 50 maximum marks, comes from arithmetical reasoning part only.
  • SSC-CGL apart, in almost every exam, a candidate could find the arithmetical reasoning and figural classification questions in abundance.
  • If practised properly, these questions may save the overall time to attempt the paper and thus, one could have more time for other questions.
  • Other forms of linear algebra and mathematical questions could be practised and solved in an easier way by practising the arithmetical reasoning and figural classification questions.

Most recommended books for arithmetical reasoning and figural classification (verbal and non-verbal reasoning)


Book Name 



Verbal & Non-Verbal Reasoning

R. S. Aggarwal


Verbal & Non-Verbal Reasoning (Hindi)

Kiran Publication


Fast Track Objective (arithmetic reasoning)

Arihant Publication


For Notes, Study Material and Online Quiz (thousands of questions to practice are available)


Why prepare arithmetical reasoning and figural classification from BYJU'S Exam Prep?

With India’s largest exam preparation platform, candidates could customize their preparation with live interactive classes, day-wise preparation plan, discussion board for clearing doubts, expert teachers with extensive experience and over 200 quizzes and tests. With the facility of BYJU'S Exam Prep Test Seriess, you could have unlimited access to all mock tests in your desired exam category. BYJU'S Exam Prep takes care of your learning and preparation, be it exam notifications, results, cut-off lists, tutoring and mentoring, providing study material, and even one-on-one discussion forums- everything from scratch to your dream job!

Frequently Asked Questions (FAQs)

1- How to solve the arithmetic problems related to ages? Provide an example.

Problems on age could also be solved by formulating the subjective question into mathematical equations. As an example, let us solve a related problem:

Rajeev's age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev?

The present problem could be solved as: Let Rajeev's present age be x years. Then,

Rajeev's age after 15 years = (x + 15) years.

Rajeev's age 5 years back = (x - 5) years.

Therefore, x + 15 = 5 (x - 5), or x + 15 = 5x – 25, or 4x = 40, or x = 10.

Hence, Rajeev's present age = 10 years.

2- Provide the solution for this figural problem?


As all other figures can be rotated into each other, the only odd one out is an option (c).

3- Find the remainder when 231 is divided by 5?

As 210 = 1024. Unit digit of 210 x 210 x 210 is 4 [as 4 x 4 x 4 gives unit digit 4].

Therefore, Unit digit of number 231 is 8. Now, 8 when divided by 5, gives 3 as remainder. Hence, 231 when divided by 5, gives 3 as remainder.

4- What will be the product of all the numbers on a telephone?

One of the numbers on the telephone will be zero which gives us the product of all the numbers as zero. 

5- What could be the proportionate image at “?” ?


Answer will be (C), as following the symmetry the image at (C) will be proportional.