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

Chapter Summary: Comprehensive Arithmetic Principles for CAT 2026

Arithmetic forms the backbone of Quantitative Aptitude for the IIM Common Admission Test (CAT). A firm grasp of these foundational concepts, shortcuts, and core algebraic relations is essential for solving high-yield exam problems efficiently.

1. Percentages, Profit, Loss & Discount

Percentage change and multiplicative factors simplify compound interest and profit calculations. Key formulas include:

• Percentage Increase/Decrease: Multiplicative factor \(F = 1 \pm \frac{x}{100}\)
• Profit & Loss: \(\text{Profit \%} = \bigl(\frac{\text{SP} - \text{CP}}{\text{CP}}\bigr) \times 100\)
• Successive Discounts: Net Discount \(= \bigl(d_1 + d_2 - \frac{d_1 \times d_2}{100}\bigr)\%\)

2. Ratios, Proportions & Mixtures

Ratio balances establish relationships between quantities, while the rule of alligation simplifies weighted averages:

• Compounded Ratio: If \(a:b\) and \(c:d\), then combined ratio is \(ac:bd\)
• Rule of Alligation: \[\frac{\text{Cheaper Quantity}}{\text{Dearer Quantity}} = \frac{d - m}{m - c}\] where \(c\) is cheaper price, \(d\) is dearer price, and \(m\) is mean price.

3. Time, Speed & Distance (TSD)

Core proportionality rules govern relative speed, circular tracks, and streams:

• Average Speed: \(S_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}}\). For equal distances: \[S_{\text{avg}} = \frac{2S_1 S_2}{S_1 + S_2}\]
• Relative Speed: Same direction = \(|S_1 - S_2|\); Opposite direction = \(S_1 + S_2\)

4. Time & Work

Work done is proportional to efficiency and time spent:

• Work Equivalence: \[M_1 D_1 H_1 E_1 = M_2 D_2 H_2 E_2\] where \(M\) = Men, \(D\) = Days, \(H\) = Hours, \(E\) = Efficiency.

5. Averages & Progressions

Averages represent central tendency, while Arithmetic Progressions (AP) track uniform increases:

• Sum of AP: \[S_n = \frac{n}{2}\bigl(2a + (n-1)d\bigr)\]
• Weighted Average: \(A_w = \frac{w_1 x_1 + w_2 x_2}{w_1 + w_2}\)