Why Shortcuts Matter in Competitive Maths

In competitive exams, you have roughly 30-60 seconds per mathematics question. Traditional methods taught in school take too long. Learning calculation shortcuts can save 10-15 minutes in your exam, which translates to 8-10 additional questions attempted.

Percentage Shortcuts

  • Finding percentages of any number: To find 15% of 840: Calculate 10% (84) + 5% (42) = 126. Break complex percentages into simpler ones.
  • Successive percentage change: If price increases by 20% then decreases by 20%, net change = -4% (not zero). Formula: a + b + ab/100.
  • Fraction equivalents: Memorize common fractions: 1/8 = 12.5%, 1/6 = 16.67%, 1/12 = 8.33%, 3/8 = 37.5%. This speeds up calculations significantly.

Multiplication Tricks

Multiplying by 11: 23 × 11 = 253 (put sum of digits in middle: 2_5_3). For numbers near 100: 97 × 96 = 9312 (subtract complement from other number for first part, multiply complements for second part: 97-4=93, 3×4=12).

Ratio and Proportion Shortcuts

  • Alligation method: Use for mixture problems, average problems, and profit-loss. Draw the cross-multiplication diagram for instant answers.
  • Componendo-Dividendo: If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d). Useful in many ratio problems.

Time, Speed, and Distance

Average speed for equal distances: Use harmonic mean = 2ab/(a+b) for two speeds. For trains crossing: Add lengths, add speeds (opposite direction) or subtract speeds (same direction). Convert km/hr to m/s by multiplying by 5/18.

Number System Tricks

  • Divisibility rules: By 4 (last 2 digits), by 8 (last 3 digits), by 11 (alternate digit sum difference)
  • Finding remainders: Use pattern recognition for powers. Example: remainder of 2^100 divided by 7 follows a cycle of 6.
  • Unit digit: Learn the cycle of unit digits for all single digits (cycle of 4 for most numbers).

Practice Strategy

Learn one shortcut per day. Practice 20 questions using that shortcut. After a week, mix all learned shortcuts in practice sets. Speed comes from muscle memory - your brain should automatically pick the fastest method for each question type.