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

Chapter Summary: Comprehensive Arithmetic Core for CAT 2026

Arithmetic constitutes the largest section of the Quantitative Aptitude module in the IIM Common Admission Test (CAT). Mastery over these concepts requires a strong grasp of foundational principles, ratio dynamics, and application-based formulas.

1. Percentages, Profit, Loss & Discount

• Percentage Change: \(\text{Percentage Change} = \bigl(\frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}}\bigr) \times 100\)
• Multiplying Factor (MF): An increase of \(x\%\) gives \(\text{MF} = 1 + \frac{x}{100}\); a decrease gives \(\text{MF} = 1 - \frac{x}{100}\).
• Profit & Loss: \(\text{Profit \%} = \bigl(\frac{\text{SP} - \text{CP}}{\text{CP}}\bigr) \times 100\); \(\text{Discount \%} = \bigl(\frac{\text{MP} - \text{SP}}{\text{MP}}\bigr) \times 100\).
• Faulty Weights: \(\text{Gain \%} = \bigl(\frac{\text{Error}}{\text{True Value} - \text{Error}}\bigr) \times 100\).

2. Ratios, Proportions & Mixtures

• Compounded Ratio: The compounded ratio of \(a:b\) and \(c:d\) is \(ac:bd\).
• Alligation Rule: \(\frac{\text{Quantity of Cheaper}}{\text{Quantity of Dearer}} = \frac{d - m}{m - c}\), where \(d\) is dearer price, \(c\) is cheaper price, and \(m\) is mean price.
• Repeated Dilution: \(\text{Final Concentration} = \text{Initial Concentration} \times \bigl(1 - \frac{x}{V}\bigr)^n\), where \(x\) is removed volume, \(V\) is total capacity, and \(n\) is operations count.

3. Time, Speed & Distance (TSD)

• Basic Relation: \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\); conversion: \(1\text{ m/s} = \frac{18}{5}\text{ km/h}\).
• Average Speed: For equal distances at speeds \(a\) and \(b\), \(\text{Average Speed} = \frac{2ab}{a + b}\).
• Relative Speed: Same direction: \(S_{\text{rel}} = |S_1 - S_2|\); Opposite direction: \(S_{\text{rel}} = S_1 + S_2\).
• Circular Tracks: First meeting time at starting point = \(\text{LCM}\bigl(\frac{L}{S_1}, \frac{L}{S_2}\bigr)\).

4. Time & Work

• Work Efficiency: \(\text{Work} = \text{Efficiency} \times \text{Time}\). If \(A\) completes work in \(a\) days and \(B\) in \(b\) days, combined rate = \(\frac{1}{a} + \frac{1}{b}\).
• Pipes & Cisterns: Inlet rate is positive, outlet/leak rate is negative.

5. Simple & Compound Interest

• Simple Interest (SI):Cumulative interest \(SI = \frac{P \times R \times T}{100}\).
• Compound Interest (CI): Amount \(A = P\bigl(1 + \frac{R}{100}\bigr)^T\). Difference for 2 years: \(CI - SI = P\bigl(\frac{R}{100}\bigr)^2\).