20 Quantitative Aptitude Shortcuts Every Aspirant Must Know

Competitive exams reward speed as much as accuracy. These 20 shortcuts can save 30–40 seconds per question — adding up to 5+ extra minutes in an hour-long test.

Percentage Shortcuts

Shortcut 1: Fraction equivalents Memorise these: 1/8 = 12.5%, 1/6 = 16.67%, 1/4 = 25%, 1/3 = 33.33%, 3/8 = 37.5%, 1/2 = 50%, 5/8 = 62.5%, 2/3 = 66.67%, 3/4 = 75%, 7/8 = 87.5%

Converts DI percentage questions into simple fraction calculations.

Shortcut 2: Successive percentage change If a value increases by A% then B%, net change = A + B + (AB/100)% Example: 20% increase then 10% increase → net = 20 + 10 + (20×10/100) = 32% increase

Shortcut 3: Percentage comparison To compare 14/28 vs 17/34 — cross multiply: 14×34=476 vs 17×28=476. Equal. Much faster than converting to percentages.

Profit & Loss Shortcuts

Shortcut 4: Markup and discount If marked up by M% and discounted by D%, net profit% = M − D − (MD/100)

Shortcut 5: Equal amounts — different rates Buying two items at same total cost: average CP = 2×(CP1×CP2)/(CP1+CP2). Harmonic mean formula.

Shortcut 6: Dishonest trader Trader uses faulty weight of x grams instead of 1000 grams and claims no profit no loss: Profit% = (1000−x)/x × 100

Ratio & Proportion

Shortcut 7: Componendo-Dividendo If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d). Saves steps in ratio equations.

Shortcut 8: Alligation formula To mix two items at prices P1 and P2 to get mixture at price M: Ratio = (P2−M) : (M−P1)

Time, Speed & Distance

Shortcut 9: Trains crossing Two trains of lengths L1 and L2, speeds S1 and S2:

Same direction: Time = (L1+L2)/(S1−S2)
Opposite direction: Time = (L1+L2)/(S1+S2)

Shortcut 10: Average speed (equal distances) Average speed = 2×S1×S2/(S1+S2) — NOT (S1+S2)/2

Shortcut 11: Relative speed Upstream speed = B−R, Downstream = B+R, where B = boat speed, R = river speed.

Time & Work

Shortcut 12: Work formula If A does work in 'a' days and B in 'b' days, together: ab/(a+b) days.

Shortcut 13: Pipe and cistern One pipe fills in A hours, another empties in B hours (B>A), net fill time = AB/(B−A).

Shortcut 14: Efficiency method Assume total work = LCM of given days. Calculate daily work units. Much faster than fraction method.

Number System

Shortcut 15: Divisibility rules

4: last 2 digits divisible by 4
8: last 3 digits divisible by 8
11: alternating digit sum difference is 0 or multiple of 11
7: double last digit, subtract from remaining digits; repeat

Shortcut 16: Units digit of powers Units digit of any number raised to a power follows a cycle of 4. Example: 7^1=7, 7^2=9, 7^3=3, 7^4=1, then repeats. Find power mod 4.

Simple & Compound Interest

Shortcut 17: CI vs SI difference For 2 years: CI − SI = P(R/100)² For 3 years: CI − SI = P(R/100)² × (R/100 + 3)

Shortcut 18: Rule of 72 Years to double at R% compound interest ≈ 72/R. At 8%: ~9 years. At 12%: ~6 years.

Algebra & Averages

Shortcut 19: Average — new member joins New average = Old average + (New value − Old average)/(New count)

Shortcut 20: (a²−b²) factoring Always factor as (a+b)(a−b). Speeds up calculations like 87²−13² = (87+13)(87−13) = 100×74 = 7400.

How to Apply These in Exam

Practice each shortcut until it becomes reflex — not just reading, but doing 20 problems each
In the exam, recognise the pattern first (e.g., "this is a successive percentage problem") before choosing the shortcut
Verify your shortcut answer with the long method for a few problems — builds confidence