How do I remember all 100 aptitude shortcuts before the exam?

Group them by topic and make a 1-page cheat sheet per section. Revise daily for 1 week before the exam. Focus on formula + 1 example per shortcut, in batches of 10–15.

100 Shortcuts to Crack Quantitative Aptitude | BharatDisha

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100 Shortcuts to Crack Quantitative Aptitude: The Ultimate Speed Guide for All Competitive Exams

Q: Can these quantitative aptitude shortcuts be used for CAT exam?

Yes, In the CAT exam Quantitative Ability section is must. This Shortcuts is helpful for speeding up in percentage, profit/loss, ratio, time-speed-distance, and permutation-combination questions so they can directly apply.

Q: How many shortcuts should I practice per day?

For beginners, focus on 3–5 shortcuts per day with 10–15 questions each. It's better to master 5 shortcuts completely than skim through 20.

Q: Which topics have the highest weightage in IBPS PO?

Data Interpretation carries the most weight (15–20 marks). After that, simplification, percentage, profit/loss, and time-speed-distance are frequently asked.

Q: What is the formula for CI minus SI for 2 years?

CI − SI = P × (R/100)² for 2 years. For 3 years: CI − SI = P × (R/100)² × (3 + R/100).

Q: Is the alligation method useful for non-mixture problems?

Yes! Alligation can be applied to average problems, profit/loss problems, and speed problems. It is one of the most versatile tricks in quantitative aptitude.

✍️ Parminder kaur preety 📅 Updated: 2025 ⏱ 18 min read 📚 IBPS • SBI • SSC • CAT • UPSC • GATE • GRE

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.

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.

Shortcut #1

Splitting a Number in a Given Ratio

Find total parts, then multiply each ratio term by (Total ÷ Sum of parts).

Formula: Part₁ = (Ratio₁ / Total Parts) × Total Number

Example: Divide 720 in ratio 2:3
Total parts = 5 → First = (2/5) × 720 = 288, Second = (3/5) × 720 = 432

Shortcut #2

Direct Proportion

Formula: A₁/A₂ = B₁/B₂ (both increase or decrease together)

Example: 2g diamond = $45,000. Price of 6g?
B₂ = 45000 × (6/2) = $1,35,000

Shortcut #3

Inverse Proportion

Formula: A₁/A₂ = B₂/B₁ (one increases, other decreases)

Example: 100cc bike → 80km mileage. 150cc bike?
B₂ = (100 × 80)/150 = 53.33 km

Shortcut #4

Finding A:C from A:B and B:C

Multiply through to get A:B:C, then read off A:C.

Example: A:B = 4:5, B:C = 3:4. A earns $3600. Find C.
A:B:C = 12:15:20 → A:C = 3:5 → C = $6,000

Shortcut #5

Chain Ratios (A:B:C:D)

Example: A:B=3:5, B:C=4:5, C:D=6:7. A=$7200. Find D.
A:B:C:D = 72:120:150:175 → A:D = 72:175 → D = $17,500

Shortcut #6

Common Factor 'x' Method

When numbers are in ratio and another condition is given, assume numbers as ratio × x and solve for x.

Example: Numbers in ratio 4:5, sum of squares = 1025.
(4x)² + (5x)² = 1025 → 41x² = 1025 → x = 5 → Numbers: 20 and 25

Shortcut #7

Finding Number of Coins

X = Total Amount ÷ [(Q₁×V₁) + (Q₂×V₂) + ...]

Example: 5p, 10p, 20p coins in ratio 2:4:5. Total = ₹4.50.
T = (2×5)+(4×10)+(5×20) = 150 paise → X = 450/150 = 3 → 20p coins = 5×3 = 15 coins

Shortcut #8

Adding/Removing Quantities in Mixture

Example: Milk:Water = 2:5. After adding 4L water, ratio = 1:3.
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.

Shortcut #9

Profit Share Ratio

P₁:P₂:P₃ = (I₁×T₁) : (I₂×T₂) : (I₃×T₃)

Example: A invests ₹5000 for 3 yrs, B joins after 1yr with ₹6000, C after 2yrs with ₹9000.
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.

Shortcut #10

Average Price of a Mixture

Aₘ = (A₁N₁ + A₂N₂) / (N₁ + N₂)

Example: Rice at ₹30/kg and ₹40/kg mixed in 2:3.
Mean price = [(30×2)+(40×3)]/5 = ₹36/kg

Shortcut #11

Alligation Rule (Finding Mix Ratio)

Cross-subtract mean price from higher and lower prices to get the ratio.

Example: Mix ₹40/kg and ₹60/kg rice to get ₹46/kg.
(60-46):(46-40) = 14:6 = 7:3

Shortcut #12

Successive Removal & Replacement

F = I × [1 − (R/I)]ⁿ
(I = initial, R = removed each time, n = times)

Example: 1000L wine. 100L removed & replaced with water, 3 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.

Shortcut #13

Common Increase/Decrease Rule

If all elements change by the same value, average changes by the same value.

Example: Family of 4, average age 34. Average after 4 years? → 38

Shortcut #14

Adding/Removing an Element

New element = (New Avg × New Count) − (Old Avg × Old Count)

Example 1: 5 students avg 18. Add teacher, new avg 20. Teacher's age?
(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

Shortcut #15

Weighted Average

A₀ = (A₁N₁ + A₂N₂ + ... + AₙNₙ) / (N₁ + N₂ + ... + Nₙ)

Example: 3 classes with averages 40, 50, 60 and 10, 20, 30 students.
Overall avg = [(40×10)+(50×20)+(60×30)]/60 = 53.33

Shortcut #16

Middle Subject Mark (Overlapping Groups)

M = A₁N₁ + A₂N₂ − A₀N₀

Example: 11 subjects avg 60. First 6 avg 50, last 6 avg 62. 6th mark?
(50×6)+(62×6)−(60×11) = 300+372−660 = 12

Shortcut #17

Middle Subject Mark (Non-Overlapping)

M = A₀N₀ − A₁N₁ − A₂N₂

Example: 9 subjects avg 75. First 4 avg 69, last 4 avg 78. 5th subject?
(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.

Shortcut #18

Basic Percentage Calculation

% = (Value / Base Value) × 100

Example: 1102 out of 1200 → (1102/1200) × 100 = 91.83%

Shortcut #19

Percentage Increase/Decrease

% Change = [(To − From) / From] × 100

Example: Salary ₹40,000 → ₹45,000 → % increase = [(5000)/40000] × 100 = 12.5%

Shortcut #20

Net Change with Two Percentage Changes

Net % = ±a ±b + [(±a)(±b)/100]

Example: Salary ₹20,000. Decreased 10%, then increased 30%.
Net = −10+30+[(−10)(30)/100] = 20−3 = +17% → New salary = ₹23,400

Shortcut #21

Final Value After Multiple Changes

Final = [(100±a)/100] × [(100±b)/100] × ... × Initial

Example: ₹30,000 with +10%, −20%, +30%
Final = (11/10)×(8/10)×(13/10) × 30,000 = ₹34,320

Shortcut #22

Equal % Increase then Decrease

Net change = a²/100 % decrease (always a net loss)

Example: Price +10% then −10% → Net = 10²/100 = 1% decrease → ₹1000 → ₹990

Shortcut #23

Steady Percentage Change (Year-on-Year)

Final = [(100±a)/100]ⁿ × Initial

Example: Population 2,00,000 grows 10% yearly for 3 years.
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.

Shortcut #24

Profit/Loss Percentage

P% or L% = [(SP − CP) / CP] × 100

Example 1: Bike CP=₹40,000, SP=₹46,000 → Profit = 15%
Example 2: Mobile CP=₹9,900, SP=₹9,000 → Loss = 9.09%

Shortcut #25

Net Profit/Loss with Two Transactions

Net % = ±a ±b + [(±a)(±b)/100]

Example: $3000 product. Sold at 10% profit, then 20% loss.
Net = 10−20+[(10×−20)/100] = −10−2 = 12% loss

Shortcut #26

Selling Price Through Multiple Hands

SP = [(100±a)/100] × [(100±b)/100] × ... × CP

Example: Watch ₹5000. A→B: 10% loss, B→C: 30% loss, C→D: 40% profit.
SP = (9/10)×(7/10)×(14/10) × 5000 = ₹4,410

Shortcut #27

Yearly Depreciation (Steady Loss)

SP = [(100−a)/100]ⁿ × CP

Example: Laptop ₹45,000. Depreciates 20% yearly. Price after 2 years?
SP = 45,000 × (0.8)² = ₹28,800

Shortcut #28

Equal Profit & Loss on Same SP

Net Loss% = a²/100 (always a net loss when SP is same)

Example: Two laptops sold at same SP — one at 50% profit, other at 50% loss.
Net loss = 50²/100 = 25% loss

Shortcut #29

Discount, Marked Price and SP

SP = [(100 − d)/100] × MP

Example: MRP ₹450, sold at ₹330.
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.

Shortcut #30

Linear Equation Method

Example: Father is twice son's age. After 5 years, sum = 100.
Let son = S, father = 2S → (2S+5)+(S+5) = 100 → S = 30 → Father = 60 years

Shortcut #31

Quadratic Equation Method

Example: Father + Son = 45, Product = 350.
S² − 45S + 350 = 0 → S = 10, Father = 35 → Difference = 25 years

Shortcut #32

Simultaneous Equations

Example: F + S = 40. After 5 years, ratio = 7:3.
F + S = 40; 3F − 7S = 20 → Son = 10, Father = 30

Shortcut #33

Common Factor 'x' in Age Ratios

x = Difference in years / Difference in ratio terms

Example: Ages were 4:3 five years ago, will be 5:4 in two years.
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:

🧠

Memorize, Don't Derive

During exam, you have 60–90 seconds per question. Never try to derive formulas on the spot.

🔄

Practice 10–15 Questions Per Shortcut

Just reading isn't enough. Muscle memory comes from repeated practice.

⚡

Identify the Shortcut First

Read the question, identify which shortcut applies, then solve. This saves 30–40 seconds.

🎯

Use Approximation When Possible

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	—

Parminder kaur preety Quantitative Aptitude Expert & Author

Author of the bestselling guide 100 Shortcuts to Crack Quantitative Aptitude. Has helped thousands of students crack IBPS, SSC, and CAT exams with his practical shortcut-based approach to maths.

❓ Frequently Asked Questions

Can these shortcuts be used for CAT exam too? +

Yes, In the CAT exam Quantitative Ability section is must. This Shortcuts is helpful for speeding up in percentage, profit/loss, ratio, time-speed-distance, and permutation-combination questions so they can directly apply.

How many shortcuts should I practice per day? +

For beginners, focus on 3–5 shortcuts per day. Practice 10–15 questions for each. It's better to master 5 shortcuts completely than skim through 20. Over 3–4 weeks, you can cover all 100 comfortably.

Which topics have the highest weightage in IBPS PO? +

In IBPS PO, Data Interpretation carries the most weight (15–20 marks). After that, simplification, percentage, profit/loss, and time-speed-distance are frequently asked. Number series and quadratic equations are also important for the prelims.

Is the alligation method useful for non-mixture problems too? +

Yes! Alligation (Shortcut #11) can be applied to average problems, profit/loss problems, and even speed problems when two groups are combined. It's one of the most versatile tricks in quantitative aptitude.

What is the formula for CI minus SI for 2 years? +

The direct shortcut is: CI − SI = P × (R/100)² for 2 years. For 3 years: CI − SI = P × (R/100)² × (3 + R/100). These eliminate the need to calculate CI and SI separately.

How do I remember all 100 shortcuts before the exam? +

Group them by topic and make a 1-page cheat sheet for each section. Focus on formula + 1 example per shortcut. Revise the cheat sheet daily for 1 week before the exam. Don't try to memorize all 100 together — break it into batches of 10–15.

100 Shortcuts to Crack Quantitative Aptitude: The Ultimate Speed Guide for All Competitive Exams

1. Ratio and Proportion

Splitting a Number in a Given Ratio

Direct Proportion

Inverse Proportion

Finding A:C from A:B and B:C

Chain Ratios (A:B:C:D)

Common Factor 'x' Method

Finding Number of Coins

Adding/Removing Quantities in Mixture

2. Partnership

Profit Share Ratio

3. Mixtures and Alligation

Average Price of a Mixture

Alligation Rule (Finding Mix Ratio)

Successive Removal & Replacement

4. Average

Common Increase/Decrease Rule

Adding/Removing an Element

Weighted Average

Middle Subject Mark (Overlapping Groups)

Middle Subject Mark (Non-Overlapping)

5. Percentage

Basic Percentage Calculation

Percentage Increase/Decrease

Net Change with Two Percentage Changes

Final Value After Multiple Changes

Equal % Increase then Decrease

Steady Percentage Change (Year-on-Year)

6. Profit, Loss and Discount

Profit/Loss Percentage

Net Profit/Loss with Two Transactions

Selling Price Through Multiple Hands

Yearly Depreciation (Steady Loss)

Equal Profit & Loss on Same SP

Discount, Marked Price and SP

7. Problems on Ages

Linear Equation Method

Quadratic Equation Method

Simultaneous Equations

Common Factor 'x' in Age Ratios

8. Time, Speed and Distance (Shortcuts #34–38)

9. Trains (Shortcuts #39–42)

10. Boats and Streams (Shortcuts #43–45)

11. Time and Work (Shortcuts #46–52)

12. Pipes and Cisterns (Shortcuts #53–56)

13. Simple and Compound Interest (Shortcuts #57–62)

14. Number System (Shortcuts #63–68)

15. HCF and LCM (Shortcuts #69–72)

16. Heights and Distances (Shortcuts #73–76)

17. Progressions (Shortcuts #77–80)

18. Calendar (Shortcuts #81–84)

19. Clocks (Shortcuts #85–88)

20. Permutation and Combination (Shortcuts #89–94)

21. Probability (Shortcuts #95–100)

🎯 Exam Strategy Tips

📚 Which Exams Use These Shortcuts?

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