IIM CAT 2026 cheat sheet for Arithmetic! 📱 Practice 1 Lakh+ PYQs on ExamBhai.com! - Free Study Material

Arithmetic Concepts & Formula Breakdown for CAT 2026

Arithmetic constitutes a foundational component of the Quantitative Aptitude section in IIM CAT 2026. This textbook summary details core definitions, essential formulas, and structural relationships across primary arithmetic domains.

1. Percentages, Profit, Loss & Interest

• Percentage Change: \(\text{Percentage Change} = \frac{\text{Absolute Change}}{\text{Base Value}} \times 100\)
• Profit & Loss: \(\text{Profit \%} = \frac{SP - CP}{CP} \times 100\) and \(\text{Discount \%} = \frac{MP - SP}{MP} \times 100\)
• Compound Interest: Compound Amount \(A = P\bigl(1 + \frac{r}{100}\bigr)^n\), where \(P\) is principal, \(r\) is annual interest rate, and \(n\) is time in years.

2. Ratios, Proportions & Alligations

• Duplicate Ratio: The duplicate ratio of \(a:b\) is defined as \(a^2:b^2\).
• Alligation Formula: \(\frac{Q_{\text{cheaper}}}{Q_{\text{dearer}}} = \frac{d - m}{m - c}\), where \(c\) represents cheaper cost, \(d\) represents dearer cost, and \(m\) represents mean mixture cost.

3. Time, Speed & Distance

• Fundamental Equation: \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\). Conversion factor: \(1 \text{ m/s} = \frac{18}{5} \text{ km/h}\).
• Average Speed: \(\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\). For two equal distance legs: \(\text{Average Speed} = \frac{2 S_1 S_2}{S_1 + S_2}\).
• Relative Speed: Objects moving in opposite directions: \(S_{\text{rel}} = S_1 + S_2\); moving in the same direction: \(S_{\text{rel}} = |S_1 - S_2|\).

4. Time & Work

• Efficiency Relationship: \(\text{Total Work} = \text{Efficiency} \times \text{Time}\). If an individual completes work in \(D\) days, one day efficiency equals \(\frac{1}{D}\).
• Pipes & Cisterns: Inlet work is positive; outlet work is negative. Net filling rate: \(\frac{1}{T_1} - \frac{1}{T_2}\).

5. Averages & Weighted Averages

• Weighted Average Formula: \(A_w = \frac{n_1 A_1 + n_2 A_2}{n_1 + n_2}\), where \(n_1, n_2\) represent group sizes and \(A_1, A_2\) represent respective subgroup averages.