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

Mastering Arithmetic Formulas for CAT 2026

Arithmetic forms the backbone of the Quantitative Aptitude section in the IIM CAT examination, accounting for a significant portion of the total questions. Mastery over fundamental formulas, concepts, and shortcut techniques enables rapid problem-solving and enhanced accuracy under strict time constraints.

1. Percentages, Profit, Loss & Discount

• Percentage Change: \(\text{Percentage Change} = \bigl(\frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}}\bigr) \times 100\)
• Profit & Loss: \(\text{Profit \%} = \bigl(\frac{SP - CP}{CP}\bigr) \times 100\), \(\text{Loss \%} = \bigl(\frac{CP - SP}{CP}\bigr) \times 100\)
• Discount & Markup: \(\text{Discount \%} = \bigl(\frac{MP - SP}{MP}\bigr) \times 100\), \(SP = MP \times \bigl(1 - \frac{D}{100}\bigr)\)

2. Simple & Compound Interest

• Simple Interest (SI): \[SI = \frac{P \times R \times T}{100}\]
• Compound Interest (CI): \[A = P \bigl(1 + \frac{R}{100}\bigr)^n, \quad CI = A - P\]
• Difference between CI and SI for 2 years: \[\text{Difference} = P \bigl(\frac{R}{100}\bigr)^2\]

3. Ratio, Proportion & Averages

• Compounded Ratio: The compounded ratio of \(a:b\) and \(c:d\) is \(ac:bd\).
• Weighted Average: \[A_{w} = \frac{w_1 A_1 + w_2 A_2 + \dots + w_n A_n}{w_1 + w_2 + \dots + w_n}\]
• Average Speed: \[\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\]

4. Time, Speed, Distance & Work

• Relative Speed: Objects moving in same direction: \(S_1 - S_2\); opposite direction: \(S_1 + S_2\).
• Work Efficiency Equation: \[\text{Work} = \text{Rate} \times \text{Time} \quad \text{or} \quad \frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}\]