Speed Math & Quantitative Aptitude Formulas Cheat Sheet

Master high-speed quantitative aptitude shortcuts, fraction to percentage conversion tables, and test formulas in our live interactive verification sandbox.

Quantitative Aptitude Cheat Sheet

Speed Math & Aptitude Formulas Hub

Instant shortcuts, fraction tables, LCM tricks & worked examples for SSC CGL, Banking, CSAT & Railway NTPC.

Fraction to Percentage Table (1/2 to 1/25)

Memorize these values for 10x faster calculations in Data Interpretation and Profit/Loss.

1/2

50%0.50

1/3

33.33%0.333

1/4

25%0.25

1/5

20%0.20

1/6

16.66% (16 2/3%)0.166

1/7

14.28% (14 2/7%)0.142

1/8

12.5%0.125

1/9

11.11% (11 1/9%)0.111

1/10

10%0.10

1/11

9.09% (9 1/11%)0.0909

1/12

8.33% (8 1/3%)0.0833

1/13

7.69%0.0769

1/14

7.14% (7 1/7%)0.0714

1/15

6.66% (6 2/3%)0.0666

1/16

6.25%0.0625

1/20

5%0.05

1/25

4%0.04

2/3

66.66% (66 2/3%)0.666

3/4

75%0.75

3/8

37.5%0.375

5/8

62.5%0.625

7/8

87.5%0.875

4/7

57.14%0.5714

Instant Formula Verification Sandbox

Discount 1 (a%):

Discount 2 (b%):

Single Equivalent Discount:28.00%

Formulas & Shortcuts (19)

percentage

Successive Percentage Change

Net Change % = a + b + (a × b) / 100

Speed Trick: If increased by a% then b%, net effect = a + b + (ab/100). Use negative sign for decreases.

Example: Length of rectangle increased by 20%, breadth decreased by 10% → Net area change = +20 - 10 + (20 × -10)/100 = 20 - 10 - 2 = +8% increase.

Exam Focus: Tested in Banking DI, SSC CGL geometry percentage questions.

percentage

Price vs Consumption (Expenditure Constant)

Reduction in consumption = [r / (100 + r)] × 100%

Speed Trick: If price rises by r%, consumption must reduce by [r / (100 + r)] × 100% to keep budget unchanged.

Example: Sugar price rises by 25% → Consumption must decrease by 25 / (100 + 25) × 100 = 25/125 × 100 = 20%.

Exam Focus: Classic 1-mark question in SSC CHSL, CGL, and Railway NTPC.

profit loss

Single Equivalent Discount for Two Successive Discounts

Single Discount = a + b - (a × b) / 100

Speed Trick: For discounts of a% and b%, direct single discount = a + b - (ab/100).

Example: Discounts of 20% and 10% → Net = 20 + 10 - (20 × 10)/100 = 30 - 2 = 28%.

Exam Focus: Repeatedly tested across all banking and SSC prelims.

profit loss

Two Articles Sold at Same SP (One x% Gain, Other x% Loss)

Overall Loss % = (x / 10)² = x² / 100 %

Speed Trick: When selling prices are equal and gain % = loss % = x, there is ALWAYS an overall loss equal to (x/10)². Never 0%!

Example: Two cows sold for ₹4,000 each: one at 20% profit, other at 20% loss → Overall loss = (20/10)² = 4%.

Exam Focus: Crucial exam trap! Aspirants mistakenly guess "no profit no loss".

profit loss

Dishonest Merchant (Faulty Weight / Cheating)

Gain % = [Error / (True Value - Error)] × 100%

Speed Trick: Gain % = [Cheated grams / Actually given grams] × 100

Example: Shopkeeper uses 900g weight instead of 1 kg (1000g) at cost price → Gain % = [100 / (1000 - 100)] × 100 = 100/900 × 100 = 11.11%.

Exam Focus: Essential SSC CGL Tier 2 concept.

interest

Difference between CI and SI for 2 Years

Difference (D) = P × (R / 100)²

Speed Trick: D = P × R² / 10,000. Alternatively, P = D × (100 / R)²

Example: P = ₹10,000, R = 10%, T = 2 years → Difference = 10,000 × (10/100)² = 10,000 × 0.01 = ₹100.

Exam Focus: Top 3 most asked formula in quantitative aptitude.

interest

Difference between CI and SI for 3 Years

Difference (D) = P × (R / 100)² × (3 + R / 100)

Speed Trick: D = [P × R² × (300 + R)] / 10,00,000

Example: P = ₹1,000, R = 10%, T = 3 years → D = [1000 × 100 × (310)] / 1,000,000 = 31,000,000 / 1,000,000 = ₹31.

Exam Focus: Appears in SBI PO, IBPS PO Mains, and SSC CGL Tier 2.

interest

Rule of 72 (Time to Double Money in CI)

Years to Double ≈ 72 / R

Speed Trick: Divide 72 by the annual interest rate to find approximate doubling time.

Example: At 8% compound interest per year, money doubles in ≈ 72 / 8 = 9 years.

Exam Focus: Great for rapid elimination of options in time-constrained exams.

time work

Two Persons Working Together (A in x days, B in y days)

Time Together = (x × y) / (x + y) days

Speed Trick: Product of days divided by Sum of days.

Example: A completes work in 10 days, B in 15 days → Together = (10 × 15) / (10 + 15) = 150 / 25 = 6 days.

Exam Focus: Foundational time & work speed calculation.

time work

Men-Days-Hours-Work Formula (MDH)

(M₁ × D₁ × H₁ × E₁) / W₁ = (M₂ × D₂ × H₂ × E₂) / W₂

Speed Trick: Everything (Men, Days, Hours, Efficiency) goes in the numerator, only Work (W) or Earnings goes in the denominator.

Example: 15 men working 8 hours/day complete 1 unit of work in 20 days. How many days will 20 men working 6 hours/day take? → (15 × 20 × 8)/1 = (20 × D₂ × 6)/1 → D₂ = 20 days.

Exam Focus: Guaranteed 1 question in SSC CGL, CHSL, MTS, and RRB Group D.

time work

Pipes & Cisterns with Emptying Leak

Net Time = (x × y) / (y - x) hours

Speed Trick: If inlet fills tank in x hrs and leak empties it in y hrs (where y > x), tank fills in xy / (y - x) hrs.

Example: Inlet pipe fills in 6 hrs, leak empties in 8 hrs → Net filling time = (6 × 8) / (8 - 6) = 48 / 2 = 24 hours.

Exam Focus: Standard pipes and cisterns problem across banking exams.

time speed-distance

Average Speed for Equal Distance (Round Trip)

Average Speed = (2 × x × y) / (x + y)

Speed Trick: Harmonic mean of speeds. NOT (x + y)/2!

Example: A car travels from A to B at 60 km/h and returns at 40 km/h → Average speed = (2 × 60 × 40) / (60 + 40) = 4800 / 100 = 48 km/h (not 50!).

Exam Focus: Most common trap question in Speed-Time-Distance.

time speed-distance

Speed Conversion (km/h ↔ m/s)

km/h to m/s: Multiply by 5/18 | m/s to km/h: Multiply by 18/5

Speed Trick: Going to smaller unit (m/s) → smaller number on top (5/18). Going to larger unit (km/h) → larger number on top (18/5).

Example: 72 km/h = 72 × (5/18) = 4 × 5 = 20 m/s.

Exam Focus: Used in every single train and race problem.

time speed-distance

Train Crossing Platform / Bridge

Time = (Length of Train + Length of Platform) / Train Speed

Speed Trick: Total distance = L_train + L_platform. When crossing a pole/man, distance is ONLY L_train.

Example: Train of 200m at 72 km/h (20 m/s) crosses a 300m platform → Time = (200 + 300) / 20 = 500 / 20 = 25 seconds.

Exam Focus: Direct formula tested in RRB NTPC, SSC CHSL.

time speed-distance

Boats & Streams (Still Water & Stream Speed)

Speed in Still Water (u) = (D + U) / 2 | Stream Speed (v) = (D - U) / 2

Speed Trick: D = Downstream speed (u + v); U = Upstream speed (u - v). Boat speed is average of D & U.

Example: Downstream = 14 km/h, Upstream = 8 km/h → Boat in still water = (14 + 8)/2 = 11 km/h; Current speed = (14 - 8)/2 = 3 km/h.

Exam Focus: Standard Boats & Streams question.

ratio alligation

Rule of Alligation (Mixing Two Quantities)

Cheaper Quantity / Dearer Quantity = (Price of Dearer - Mean Price) / (Mean Price - Price of Cheaper)

Speed Trick: (d - m) / (m - c). Cross-subtract to get mixing ratio.

Example: Tea at ₹60/kg mixed with tea at ₹75/kg to get blend worth ₹65/kg → Ratio = (75 - 65) / (65 - 60) = 10 / 5 = 2 : 1.

Exam Focus: Key shortcut for mixtures, averages, and weighted average problems.

ratio alligation

Repeated Dilution & Replacement Formula

Remaining Quantity of Pure Liquid = Initial Quantity × [1 - (x / Initial Quantity)]ⁿ

Speed Trick: Liquid left = Q × [1 - x/Q]ⁿ, where x is quantity drawn each time, and n is number of operations.

Example: A vessel contains 40 liters of milk. 4 liters drawn out and replaced with water, repeated twice (total 2 times) → Milk left = 40 × (1 - 4/40)² = 40 × (9/10)² = 40 × 81/100 = 32.4 liters.

Exam Focus: Crucial question in Banking Mains and SSC CGL Tier 2.

mensuration

Circle & Semi-Circle Essentials

Circle Area = πr² | Perimeter = 2πr | Semi-circle Perimeter = (π + 2)r = (36/7)r

Speed Trick: Remember: Perimeter of semi-circle is (36/7)r, NOT πr!

Example: Semi-circle with radius 7 cm → Perimeter = (36/7) × 7 = 36 cm.

Exam Focus: Semi-circle perimeter is the #1 trick question in 2D mensuration.

mensuration

3D Cylinder, Cone & Sphere Ratios

Cylinder Vol = πr²h | Cone Vol = (1/3)πr²h | Sphere Vol = (4/3)πr³ | Hemisphere TSA = 3πr²

Speed Trick: Cone volume is exactly 1/3 of Cylinder volume with same radius and height.

Example: Total Surface Area of solid hemisphere with radius 7 cm = 3 × (22/7) × 7² = 3 × 22 × 7 = 462 cm².

Exam Focus: Repeatedly tested in SSC CGL, CDS, and RRB NTPC.

Speed Math & Quantitative Aptitude Strategy for Banking & SSC

In competitive exams like SBI PO, IBPS PO, RRB NTPC, and SSC CGL, speed is the ultimate differentiator. Candidates have an average of 36 to 50 seconds per question. Relying on traditional school arithmetic formulas leads to time running out in the quantitative aptitude section.

Fraction Reciprocals

Knowing that 1/7 = 14.28% and 1/8 = 12.5% allows you to solve Data Interpretation sets in seconds without long division.

Difference Formulas

Instead of calculating full CI and SI separately, use D = P × (R/100)² for 2 years to solve problems in one step.

Alligation & Mixtures

The alligation rule replaces complex algebraic equations across averages, profit/loss, simple interest, and mixtures.

Quantitative Aptitude: Frequently Asked Questions

Why is memorizing fraction-to-percentage tables essential for bank exams?

In Banking Data Interpretation (tables, pie charts, bar graphs), percentages frequently involve values like 16.66%, 37.5%, 62.5%, or 87.5%. Converting them instantly to 1/6, 3/8, 5/8, and 7/8 turns cumbersome multiplications into simple divisions, saving over 5 minutes per paper.

What is the formula for the difference between Compound Interest and Simple Interest for 2 years?

For 2 years, the difference between CI and SI on principal P at rate R% is given by: Difference = P × (R / 100)². For 3 years, the formula is: Difference = P × (R / 100)² × (3 + R / 100).

When two articles are sold at the same price, one at x% profit and one at x% loss, what is the net result?

There is ALWAYS an overall loss. The overall loss percentage is calculated directly as: Loss % = (x / 10)² = x² / 100 %. For example, if two items are sold at the same price, one at 20% gain and the other at 20% loss, the net loss is (20/10)² = 4%.

How do you convert km/h to m/s and vice versa?

To convert from km/h to m/s, multiply by 5/18. To convert from m/s to km/h, multiply by 18/5. A quick memory rule: when converting to the smaller unit (m/s), put the smaller number (5) on top.