Introduction
The Arithmetic subtopic within Quantitative Aptitude is the backbone of the RPSC examination’s numerical ability section. Over the years, a substantial number of questions — 36 in the available dataset alone — have been drawn from this domain, covering a wide spectrum of concepts including number series, ratio and proportion, mixtures and alligations, percentages, simple and compound interest, time and work, probability, permutation–combination, and data interpretation. The level of difficulty ranges from straightforward application of formulas to multi-step reasoning problems that test both speed and conceptual clarity.
Why does this matter for RPSC aspirants? First, Arithmetic questions consistently appear across all tiers of the examination — from the Preliminary to the Main exams — and they carry significant weight in the overall Quantitative Aptitude score. Second, the patterns observed in the previous year questions (PYQs) reveal that RPSC tends to repeat certain question types (e.g., mixture problems with two-step operations, series based on cubes or primes, CI vs SI difference problems, and combinatorial selection with “at least one” condition). Third, mastering these core concepts builds a strong foundation for more advanced topics like algebra, geometry, and data sufficiency.
In this chapter, you will learn every concept that has been tested, from first principles. We will define all key terms, derive important formulas, walk through step-by-step examples using actual PYQs, and identify the subtle traps that separate high-scorers from the rest. By the end, you will be equipped not only to solve the 36 questions provided but also to handle any variation RPSC may introduce in future exams.
Core Concepts & Foundations
Before diving into specific problem types, you must internalise the fundamental building blocks that underpin every arithmetic operation tested. Each key term is defined below in a blockquote for quick reference. Read these carefully — they are the vocabulary of the chapter.
Ratio: A comparison of two or more quantities of the same kind by division. The ratio of a to b is written as a : b, meaning a/b. Ratios have no unit and can be simplified by dividing both terms by their greatest common divisor.
Proportion: An equation stating that two ratios are equal. If a : b = c : d, then a, b, c, d are in proportion, and ad = bc. Proportions are used to solve problems involving direct or inverse variation.
Percentage: A fraction or ratio expressed out of 100, denoted by the symbol %. x% means x/100. Percentages are used to express increase, decrease, profit, loss, discounts, and interest rates.
Simple Interest (SI): Interest calculated only on the original principal amount for the entire period. Formula: SI = (P × R × T) / 100, where P is principal, R is rate per annum, T is time in years. Amount = P + SI.
Compound Interest (CI): Interest calculated on the principal plus any previously earned interest. For annual compounding: Amount = P (1 + R/100)^T. CI = Amount – P. For non-annual compounding, the rate and time are adjusted accordingly.
Mixture and Alligation: The process of mixing two or more substances to obtain a desired concentration. Alligiation is a technique to find the ratio in which ingredients are mixed, using the rule: (Strength of cheaper) : (Strength of dearer) = (Mean strength – Cheaper) : (Dearer – Mean). It works for prices, percentages, and ratios.
Sequence and Series: An ordered list of numbers following a definite pattern (sequence). The sum of terms of a sequence is a series. Common patterns in RPSC include arithmetic progressions, geometric progressions, prime-based, cube-based, square-based, and mixed patterns.
Permutation: The number of ways to arrange a set of distinct objects in a specific order. Formula: nPr = n! / (n–r)! , where n is total objects, r is number selected.
Combination: The number of ways to select a subset of objects without regard to order. Formula: nCr = n! / [r!(n–r)!].
Probability: The measure of the likelihood of an event. For equally likely outcomes, Probability = (Number of favourable outcomes) / (Total number of outcomes). Ranges from 0 (impossible) to 1 (certain).
Time and Work: Problems relate the time taken by individuals or groups to complete a task. The fundamental principle: Work = Rate × Time. If A does a job in d days, A’s one-day work = 1/d. Combined work rates add up.
Wages and Share: Wages are proportional to the work done and the time worked. If workers are paid in a given ratio, their daily wages can be deduced by dividing the total wage by the sum of ratio units.
All of these concepts will be applied repeatedly in the deep-dive sections that follow. The key is not merely to memorise formulas but to understand the logic behind them — especially for compound interest and mixture problems, where RPSC often introduces twists like partial investment at different interest types or successive mixtures.