100 Shortcuts to Crack Quantitative Aptitude: The Ultimate Speed Guide for All Competitive Exams
Quantitative aptitude is the one section that can make or break your competitive exam result. Most students spend 3–4 minutes on a single problem — and that's where they lose. These 100 quantitative aptitude shortcuts will help you solve the same problems in under 60 seconds, once you practice them properly.
Whether you're preparing for IBPS PO, SBI Clerk, SSC CGL, CAT, UPSC CSAT, GATE, or campus placements — these shortcuts work everywhere. Aur ek baat — just reading isn't enough. Practice each shortcut with at least 10–15 questions to make it automatic.
Pro Tip: Speed matters, but accuracy matters more. A shortcut used wrong is worse than no shortcut at all. Practice first, then speed up.
- Ratio and Proportion (Shortcuts #1–8)
- Partnership (Shortcut #9)
- Mixtures and Alligation (Shortcuts #10–12)
- Average (Shortcuts #13–17)
- Percentage (Shortcuts #18–23)
- Profit, Loss and Discount (Shortcuts #24–29)
- Problems on Ages (Shortcuts #30–33)
- Time, Speed and Distance (Shortcuts #34–38)
- Trains (Shortcuts #39–42)
- Boats (Shortcuts #43–45)
- Time and Work (Shortcuts #46–52)
- Pipes and Cisterns (Shortcuts #53–56)
- Simple and Compound Interest (Shortcuts #57–62)
- Number System (Shortcuts #63–68)
- HCF and LCM (Shortcuts #69–72)
- Heights and Distances (Shortcuts #73–76)
- Progressions (Shortcuts #77–80)
- Calendar (Shortcuts #81–84)
- Clocks (Shortcuts #85–88)
- Permutation and Combination (Shortcuts #89–94)
- Probability (Shortcuts #95–100)
- Exam Strategy Tips
- Recommended Exams
- FAQs
1. Ratio and Proportion
Ratio questions are everywhere — from number problems to salary comparisons. Once you understand these shortcuts, most ratio questions become direct calculations.
Splitting a Number in a Given Ratio
Find total parts, then multiply each ratio term by (Total ÷ Sum of parts).
Total parts = 5 → First = (2/5) × 720 = 288, Second = (3/5) × 720 = 432
Direct Proportion
B₂ = 45000 × (6/2) = $1,35,000
Inverse Proportion
B₂ = (100 × 80)/150 = 53.33 km
Finding A:C from A:B and B:C
Multiply through to get A:B:C, then read off A:C.
A:B:C = 12:15:20 → A:C = 3:5 → C = $6,000
Chain Ratios (A:B:C:D)
A:B:C:D = 72:120:150:175 → A:D = 72:175 → D = $17,500
Common Factor 'x' Method
When numbers are in ratio and another condition is given, assume numbers as ratio × x and solve for x.
(4x)² + (5x)² = 1025 → 41x² = 1025 → x = 5 → Numbers: 20 and 25
Finding Number of Coins
T = (2×5)+(4×10)+(5×20) = 150 paise → X = 450/150 = 3 → 20p coins = 5×3 = 15 coins
Adding/Removing Quantities in Mixture
2x/(5x+4) = 1/3 → x = 4 → Milk = 8 litres
2. Partnership
Partnership problems are directly linked to ratio logic. Profit is divided in proportion to Investment × Time. Simple, once you get it.
Profit Share Ratio
Ratio = 15000:12000:9000 = 5:4:3
3. Mixtures and Alligation
Alligation is one of the most useful tricks — it lets you find the mixing ratio without any lengthy calculation.
Average Price of a Mixture
Mean price = [(30×2)+(40×3)]/5 = ₹36/kg
Alligation Rule (Finding Mix Ratio)
Cross-subtract mean price from higher and lower prices to get the ratio.
(60-46):(46-40) = 14:6 = 7:3
Successive Removal & Replacement
(I = initial, R = removed each time, n = times)
F = 1000 × (0.9)³ = 729L wine, Water = 271L
4. Average
Average questions look complex but become easy with the right approach. These shortcuts handle common scenarios you'll see in almost every exam.
Common Increase/Decrease Rule
If all elements change by the same value, average changes by the same value.
Adding/Removing an Element
(20×6) − (18×5) = 120 − 90 = 30 years
Example 2: 40 bags avg 20kg. Remove 1 bag, avg becomes 19.5. Bag weight?
(20×40) − (19.5×39) = 800 − 760.5 = 39.5 kg
Weighted Average
Overall avg = [(40×10)+(50×20)+(60×30)]/60 = 53.33
Middle Subject Mark (Overlapping Groups)
(50×6)+(62×6)−(60×11) = 300+372−660 = 12
Middle Subject Mark (Non-Overlapping)
(75×9)−(69×4)−(78×4) = 675−276−312 = 87
5. Percentage
Percentage is the backbone of many aptitude topics — profit/loss, interest, data interpretation. Master these, and half your problems get easier.
Basic Percentage Calculation
Percentage Increase/Decrease
Net Change with Two Percentage Changes
Net = −10+30+[(−10)(30)/100] = 20−3 = +17% → New salary = ₹23,400
Final Value After Multiple Changes
Final = (11/10)×(8/10)×(13/10) × 30,000 = ₹34,320
Equal % Increase then Decrease
Steady Percentage Change (Year-on-Year)
Final = 2,00,000 × (1.1)³ = 2,66,200
6. Profit, Loss and Discount
In every banking and SSC exam, you'll find 3–5 questions on this topic. These shortcuts directly give you answers without building equations.
Profit/Loss Percentage
Example 2: Mobile CP=₹9,900, SP=₹9,000 → Loss = 9.09%
Net Profit/Loss with Two Transactions
Net = 10−20+[(10×−20)/100] = −10−2 = 12% loss
Selling Price Through Multiple Hands
SP = (9/10)×(7/10)×(14/10) × 5000 = ₹4,410
Yearly Depreciation (Steady Loss)
SP = 45,000 × (0.8)² = ₹28,800
Equal Profit & Loss on Same SP
Net loss = 50²/100 = 25% loss
Discount, Marked Price and SP
Discount = [(120)/450] × 100 = 26.67%
7. Problems on Ages
Age problems are all about forming the right equation quickly. These shortcuts reduce guesswork to zero.
Linear Equation Method
Let son = S, father = 2S → (2S+5)+(S+5) = 100 → S = 30 → Father = 60 years
Quadratic Equation Method
S² − 45S + 350 = 0 → S = 10, Father = 35 → Difference = 25 years
Simultaneous Equations
F + S = 40; 3F − 7S = 20 → Son = 10, Father = 30
Common Factor 'x' in Age Ratios
Year difference = 7, Ratio diff = 1 → x = 7 → Present ages: MS = 34, VK = 26
8. Time, Speed and Distance (Shortcuts #34–38)
Speed = Distance / Time is the core. But these derived formulas save you from lengthy algebra.
| Formula | Use When |
|---|---|
| Speed = Distance / Time | Basic calculation |
| Relative Speed (same dir) = S₁ − S₂ | Two objects moving same way |
| Relative Speed (opp dir) = S₁ + S₂ | Two objects approaching |
| Avg Speed (equal dist) = 2S₁S₂/(S₁+S₂) | Same distance, different speeds |
| Time to meet = Distance / Relative Speed | Meeting point problems |
9. Trains (Shortcuts #39–42)
| Scenario | Formula |
|---|---|
| Cross a pole/person | Time = Length of Train / Speed |
| Cross a platform/bridge | Time = (Train + Platform length) / Speed |
| Two trains cross each other | Time = (L₁ + L₂) / Relative Speed |
| Same direction | Relative Speed = S₁ − S₂ |
| Opposite direction | Relative Speed = S₁ + S₂ |
10. Boats and Streams (Shortcuts #43–45)
| Formula | Meaning |
|---|---|
| Downstream = B + S | Going with current |
| Upstream = B − S | Going against current |
| Boat speed = (Down + Up) / 2 | Speed in still water |
| Stream speed = (Down − Up) / 2 | Speed of current |
11. Time and Work (Shortcuts #46–52)
Agar kisi kaam mein ek insaan n days leta hai, toh ek din mein woh 1/n kaam karta hai. This basic idea powers all time-and-work shortcuts.
| Formula | Use |
|---|---|
| Work rate = 1/n per day | 1 person finishes in n days |
| Combined rate = sum of individual rates | Multiple workers |
| M₁D₁ = M₂D₂ | Same work, different teams |
| M₁D₁H₁ = M₂D₂H₂ | With working hours |
| Efficiency ratio method | When ratio given instead of days |
12. Pipes and Cisterns (Shortcuts #53–56)
| Formula | Use |
|---|---|
| Fill pipe = +1/n per hour | Fills tank in n hours |
| Empty pipe = −1/n per hour | Drains tank in n hours |
| Net rate = sum of all pipe rates | Multiple pipes working together |
| Total time = 1 / Net rate | How long to fill/empty |
13. Simple and Compound Interest (Shortcuts #57–62)
| Formula | Note |
|---|---|
| SI = (P × R × T) / 100 | Simple Interest |
| A = P(1 + R/100)ⁿ | Compound Interest |
| CI − SI (2yr) = P(R/100)² | Shortcut for 2-year diff |
| CI − SI (3yr) = P(R/100)²×(3+R/100) | Shortcut for 3-year diff |
14. Number System (Shortcuts #63–68)
Key concepts: Divisibility rules (2, 3, 4, 5, 6, 8, 9, 11), unit digit patterns for powers, number of factors formula, sum of factors formula based on prime factorization.
Factors Formula: If N = aˣ × bʸ × cᶻ → Number of factors = (x+1)(y+1)(z+1)
15. HCF and LCM (Shortcuts #69–72)
| Formula | Use |
|---|---|
| HCF × LCM = Product of two numbers | Finding unknown HCF or LCM |
| HCF of fractions = HCF(num)/LCM(den) | Fractions |
| LCM of fractions = LCM(num)/HCF(den) | Fractions |
16. Heights and Distances (Shortcuts #73–76)
These questions use standard trigonometric ratios. Memorize this table — it's asked directly in many exams:
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | ∞ |
17. Progressions (Shortcuts #77–80)
| Formula | Type |
|---|---|
| AP nth term: aₙ = a + (n−1)d | Arithmetic Progression |
| AP Sum: Sₙ = n/2 × [2a + (n−1)d] | AP |
| GP nth term: aₙ = arⁿ⁻¹ | Geometric Progression |
| GP Sum: Sₙ = a(1−rⁿ)/(1−r) for r<1 | GP |
18. Calendar (Shortcuts #81–84)
Odd days concept: Remainder when total days divided by 7.
Leap year: Divisible by 4, not by 100 unless also by 400.
Century odd days: 100 years = 5, 200 years = 3, 300 years = 1, 400 years = 0.
19. Clocks (Shortcuts #85–88)
| Formula | Use |
|---|---|
| Angle = |30H − 5.5M| | Angle between clock hands |
| Hands coincide every ~65.45 min | Overlap times |
| Right angle = 15-min space apart | Perpendicular hands |
| Opposite = 30-min space | Straight line (180°) |
20. Permutation and Combination (Shortcuts #89–94)
| Formula | When to Use |
|---|---|
| ⁿPr = n!/(n−r)! | Order matters |
| ⁿCr = n!/[r!(n−r)!] | Order doesn't matter |
| Circular = (n−1)! | Circular arrangement |
| With repetition = nʳ | Repeated items allowed |
21. Probability (Shortcuts #95–100)
| Formula | Concept |
|---|---|
| P(A) = Favourable/Total outcomes | Basic probability |
| P(A') = 1 − P(A) | Complementary event |
| P(A∩B) = P(A) × P(B) | Independent events |
| P(A∪B) = P(A) + P(B) | Mutually exclusive events |
🎯 Exam Strategy Tips
Shortcuts save time — but only if you know when to apply them. Here's how to use these effectively in the actual exam:
During exam, you have 60–90 seconds per question. Never try to derive formulas on the spot.
Just reading isn't enough. Muscle memory comes from repeated practice.
Read the question, identify which shortcut applies, then solve. This saves 30–40 seconds.
If answer choices are far apart, approximate. Exact calculation isn't always needed.
📚 Which Exams Use These Shortcuts?
These shortcuts are relevant for virtually every competitive exam that has a quantitative aptitude section:
| Banking | SSC | UPSC | Management | Engineering |
|---|---|---|---|---|
| IBPS PO | CGL | CSAT | CAT | GATE |
| IBPS Clerk | CHSL | CAPF | MAT | TANCET |
| SBI PO | MTS | CDS | XAT | GRE |
| RBI Grade B | CBI | NDA | GMAT | — |