
Vedic Mathematics - Multiplication with a Series of 9’s
1. Multiplying a Number with an Equal Number of 9’s
2. Multiplying a Number by a Number with More 9’s
3. Multiplying a number by a number containing fewer 9’s
Learn to multiply by a series of ones, such as 11, 111, and 1111, by adding digits with carries and zeros on both sides; zeros are one less than ones.
Identify the repeating and nonrepeating digits, then form the fraction using nine for repeats and zero for nonrepeats. Apply the shortcut to convert 0.3 bar to 1/3 and similar cases.
Explore factorials and learn how to count trailing zeros by tallying factors of five, using division shortcuts, and determine the highest power of ten.
Explore methods to compute the highest common factor (SCF) of numbers—prime factorization, division, and shortcut—and identify co-prime pairs with practical examples.
Find the greatest number that divides several values with the same remainder by subtracting the remainder and using the greatest common divisor of the pairwise differences.
Learn to determine the HCF when remainders differ, by subtracting the remainders, using the difference, and applying divisibility checks to identify the SCF.
discover methods to identify the largest or smallest n-digit numbers with prescribed remainders when divided by multiple divisors, using the lcm, divisibility checks, and remainder patterns.
Apply real-life applications of LCM and SCF to bell timing, timber lengths divided into equal planks, and milk packaging, clarifying the distinction between LCM and SCF.
Learn shortcuts to find averages, especially for arithmetic progressions, using middle term or the average of the first and last terms, with examples from natural numbers, odd numbers, and squares.
Compute the percentage error when multiplying by 3 then 5 instead of 5 then 3, using the difference over the original and getting 64% or 44%.
Learn to solve exam based problems by calculating passing marks from percentages, comparing scores to the passing threshold, and determining maximum marks.
Learn to solve two-candidate election problems by converting vote percentages into total votes, handling casting, valid, and invalid votes, and calculating margins of victory.
Master the basics of profit and loss by learning the cost price, selling price, and marked price. Apply key formulas to compute discount, profit percentage, and related price relations.
Explore basic questions on cost price and selling price, including calculating loss and profit percentages, applying cp and sp formulas, and solving gain or loss scenarios with practical examples.
Learn to determine profit or loss and their percentages when the cost price of x items equals the selling price of y items, using cp, sp, and simple ratio methods.
Learn to calculate discounts from free articles in offers like buy one get one free and buy five get three free, avoiding common mistakes with the correct base.
Explore time and work concepts, linking duration and efficiency, and learn to compute combined work rates using lcm and fractions through A, B, and C example problems.
Solve partial work problems by calculating combined efficiencies, days of joint work, and remaining work to determine total time or solo completion for two workers A and B.
Explore work problems on alternate days, where A and B alternate on odd and even days, and learn to compute joint efficiency, fractions of days, and LCM-based solutions.
Learn to treat destruction as negative work, compute daily units and combined efficiency, and determine time to complete tasks in time and work problems.
Master the chain rule for work and time problems by relating workers, days, and work amount, with examples using men, pumps, bottles, cows, meals, and examiners.
Apply the chain rule to time and work problems with changing crews. Solve scenarios of soldiers and food provisions to predict days remaining with more or fewer workers.
Learn to solve tank filling problems by computing individual and combined pipe efficiencies, determining full and partial fill times, and handling staged shutoffs using unit-based calculations.
Master pipe efficiency problems by analyzing rate ratios, calculating combined work, and determining individual fill times using scenarios such as 3:1 and 1:5 efficiency and 32 to 42 minute fills.
Learn how to solve alternate-minute work problems with multiple workers, using lcm and combined efficiency to find total work and fill times for a tank.
Compute average speed for equal distances using the formula 2xy/(x+y), where x and y are speeds. Apply it by total time d/x + d/y and total distance 2d.
Master late–early arrival problems by applying the speed-difference formula, S1*S2/(S1−S2), multiplied by the time difference, and recognizing inverse speed–time relationships with proper unit conversion.
Delve into change in time gap due to relative speed, solving distance and speed problems where two objects move toward each other, using intervals and ratios to find meeting points.
Explore relative speed in train problems, learn when to add or subtract speeds for opposite or same directions, and solve time-distance questions with practice examples.
Learn how a train crossing a standing object covers a distance equal to its length, and compute speed as distance divided by time, with unit conversions.
Learn train crossing with a length object. Compute distance as the sum of lengths, apply relative speed (difference for same direction, sum for opposite), and convert speeds to find time.
explain upstream and downstream motion, and define speed of boat and steam with formulas: upstream = boat minus steam, downstream = boat plus steam, and boat speed = (downstream+upstream)/2.
Learn to compute boat speed in still water from downstream and upstream speeds, estimate current speed, and solve downstream and upstream distance–time problems.
Compute current speed and boat speed from downstream and upstream data using ratio. Learn formulas for current speed and boat speed, and solve downstream-upstream ratio problems with practical examples.
This course develops the essential numerical and analytical skills needed for competitive exams, campus placements, and professional assessments. It covers a wide range of topics such as arithmetic, algebra, number systems, percentages, ratios, time and work, speed and distance, and probability.
Through structured lessons, practice exercises, and test-style questions, students learn to solve problems quickly and accurately. The course focuses on building strong fundamentals, improving calculation speed, and developing logical reasoning alongside quantitative skills.
By the end of the course, students will be able to approach quantitative problems with confidence, apply shortcut methods where appropriate, and manage time effectively during exams.
Key Features:
Comprehensive coverage of core quantitative topics
Step-by-step explanations with practical examples
Tips and shortcuts to improve speed and accuracy
Regular quizzes and mock tests for self-assessment
Suitable for competitive exams, placements, and aptitude tests
1. Vedic Mathematics (Speed Maths Techniques)
Multiplication with series of 9's
Multiplication with series of 1's
Two-digit and three-digit multiplication
Squaring numbers
Square roots of perfect squares
Square roots of non-perfect squares
2. Number System
Decimal to fraction conversion
Factorials
Divisibility rules
Unit digit concepts
Remainder theorem
Positive and negative remainders
Cancellation rule
Remainders involving factorials
3. LCM & HCF
LCM concepts
HCF concepts
Same remainder problems
Different remainder problems
Product of two numbers property
HCF & LCM of fractions
Largest and smallest n-digit numbers
Real-life applications
4. Average
Basic concepts
Average calculations
Weighted average
Increase and decrease in average
Replacement problems
Wrong entry and error in data
Miscellaneous questions
5. Percentage
Percentage fundamentals
Comparison-based problems
Successive percentage changes
Percentage error
Budget-based questions
Exam-oriented problems
Venn diagram applications
Direct and successive distribution
Election-based problems
6. Profit & Loss
Cost price and selling price
Profit and loss calculations
Cost of x items = Selling price of y items
Partial selling problems
Change in cost price and selling price
Same selling price and different cost prices
Profit based on number of articles
Free articles
False weight (Dishonest Shopkeeper)
Discount
Relationship between cost price, selling price and discount
7. Time & Work
Work and efficiency concepts
Work done together
Partial work
Alternate day work
Wages
Negative work
Constructive and destructive work
Chain rule
Variable workforce problems
8. Pipes & Cisterns
Pipe efficiency
Filling and emptying tanks
Partial filling problems
Inlet and outlet pipes
Alternate minute working
Tank capacity problems
9. Time, Speed & Distance
Relationship between speed, time and distance
Speed conversions
Average speed
Fractional speed problems
Early and late arrival
Relative speed
Constant time concept
10. Problems on Trains
Relative speed
Crossing stationary objects
Crossing platforms
Crossing moving persons
Crossing moving trains
11. Boats & Streams
Upstream and downstream concepts
Finding speed and time
Return journey problems
Ratio-based questions
12. Races
Basic race concepts
Relative speed in races
Winning margin problems
Race-based applications
13. Ratio & Proportion
Basic ratios
Compound and combined ratio
Money distribution
Income, expenditure and savings
Partnership
Problems on ages
Practice sets
14. Mixture & Alligation
Ratio method
Replacement method
Addition and removal of liquids
Combined profit and loss
Mixing two or more solutions
Multiple replacement problems
Advanced practice questions
15. Simple Interest & Compound Interest
Simple interest concepts
Changing principal and rate
Amount-based problems
Different interest rates
Doubling and tripling time
Compound interest concepts
Relationship between SI and CI
16. Permutation & Combination
Fundamental principle of counting
Permutation vs Combination
Number arrangements
Word arrangements
Circular arrangements
Rank of words
Distribution problems
Geometry-based combinations
Practice questions
17. Probability
Basic probability concepts
Coin problems
Dice problems
Card problems
Balls and marbles
18. Data Sufficiency
Basic data sufficiency
Advanced data sufficiency techniques
1. Vedic Mathematics (Speed Maths Techniques)
Fast multiplication (by 9’s, by 11, base method)
Squaring shortcuts
Rapid division and finding remainders
Cross-checking answers with digital roots
1. Number System
Properties of numbers (even, odd, prime, composite)
Divisibility rules
Factors and multiples
LCM and HCF
Remainders, unit digit, last digit
Cyclicity and digital sum
3. Simplification & Approximation
BODMAS operations
Square roots and cube roots
Simplifying fractions and decimals
Approximating quickly for large numbers
4. Ratio, Proportion & Partnership
Direct and inverse proportion
Mixing problems
Partnership and profit sharing
5. Percentages
Basic percentage calculations
Increase/decrease
Comparing quantities using percentages
6. Profit, Loss & Discount
Marked price, cost price, selling price
Successive discounts and gains
False weights problems
7. Simple Interest & Compound Interest
Interest over different time periods
Difference between CI and SI
Annual, half-yearly, and quarterly compounding
8. Time, Speed & Distance
Relative speed
Trains, boats, and streams
Average speed problems
9. Time & Work
Work efficiency and ratios
Pipes and cisterns
Wages and sharing of work
10. Average
Weighted averages
Successive averages
11. Mixture & Alligation
Mixing liquids or solids
Profit & loss in mixtures
12. Algebra
Linear equations
Quadratic equations
Simplifying expressions
13. Geometry & Mensuration
Lines, angles, and triangles
Circles and polygons
Areas, volumes, and surface areas
14. Permutations, Combinations & Probability
Counting principles
Arrangements and selections
Basic probability problems
15. Data Interpretation
Tables, bar graphs, line graphs
Pie charts
Data comparison and analysis
16. Data Sufficiency
Deciding if given data is enough to answer a question
17. Sequences & Series
Arithmetic progression (AP)
Geometric progression (GP)
Special number patterns
18. Statistics
Mean, median, mode
Standard deviation (basic level)
19. Clocks & Calendars
Finding angles between hands of a clock
Time gained or lost by a clock
Odd days and day-of-week problems
20. Miscellaneous / Higher Level
Inequalities
Logarithms
Surds and indices
Simplified equations involving multiple concepts