Quantitative Aptitude: Arithmetic¶

Arithmetic questions test speed, calculation tricks, and problem-solving fundamentals.

Core Topics & Important Formulas¶

1. Percentages¶

• Base value fraction conversions:
• \(\frac{1}{2} = 50\%\), \(\frac{1}{3} = 33.33\%\), \(\frac{1}{4} = 25\%\), \(\frac{1}{5} = 20\%\)
• \(\frac{1}{6} = 16.66\%\), \(\frac{1}{7} = 14.28\%\), \(\frac{1}{8} = 12.5\%\), \(\frac{1}{9} = 11.11\%\)
• \(\frac{1}{11} = 9.09\%\), \(\frac{1}{12} = 8.33\%\), \(\frac{1}{16} = 6.25\%\)
• Successive percentage change: $\(Net \% = a + b + \frac{ab}{100}\)$

2. Profit, Loss & Discount¶

• \(Profit = SP - CP\), \(Loss = CP - SP\)
• \(Profit\% = \frac{SP - CP}{CP} \times 100\)
• \(Markup\% = \frac{MP - CP}{CP} \times 100\)
• \(Discount\% = \frac{MP - SP}{MP} \times 100\)
• Relation between CP and MP with discount \(d\%\) and profit \(p\%\): $\(\frac{CP}{MP} = \frac{100 - d}{100 + p}\)$

3. Ratio, Proportion & Mixture¶

• Compounded ratio, Duplicate ratio, Sub-duplicate ratio.
• Alligation Rule: $\(\frac{Q_1}{Q_2} = \frac{Price_2 - Mean}{Mean - Price_1}\)$

4. Time, Speed & Distance¶

• \(Speed = \frac{Distance}{Time}\)
• \(km/h\) to \(m/s\): Multiply by \(\frac{5}{18}\)
• \(m/s\) to \(km/h\): Multiply by \(\frac{18}{5}\)
• Average speed for equal distance at speeds \(x\) and \(y\): $\(Avg = \frac{2xy}{x+y}\)$
• Trains crossing poles vs platforms:
• Pole/Man: Distance = Length of Train
• Platform/Bridge: Distance = Length of Train + Length of Platform

5. Time & Work & Pipes¶

• Work = Efficiency \(\times\) Time
• Concept of LCM method for total work.
• Negative work by leakage pipes.

6. Simple Interest & Compound Interest¶

• \(SI = \frac{P \times R \times T}{100}\)
• \(CI = P \left(1 + \frac{R}{100}\right)^T - P\)
• Difference between CI and SI for 2 years: $\(Diff_2 = P \left(\frac{R}{100}\right)^2\)$
• Difference between CI and SI for 3 years: $\(Diff_3 = P \left(\frac{R}{100}\right)^2 \left(\frac{300 + R}{100}\right)\)$