Learn to identify the least common multiple by using multiples, divisors, and factors. Apply prime numbers and common multiples with examples like 4, 8, and 12 to find 24.

Master lcm basics: eliminate factors, use multiples to find lcm of two or more numbers, note prime cases as products, and apply to division with equal remainders.

Master LCM basics with worked problems: compute LCMs such as 120 and 450, find nearest multiples to 10000, and obtain the least square multiple divisible by 16, 20, and 24.

Master LCM and remainder problems with elimination methods, stepwise LCM calculations, and finding numbers with specific remainders for divisibility by 4, 6, 8, 12, 16, and more.

Learn how to compute the highest common factor (hcf) or Hatzius using long division and a minimum difference method, with 12, 18, 24 and related examples.

Learn to find the greatest common factor of numbers using the minimum-difference method and divisibility checks, with examples like gcd of 200 and 320 and other sets.

Explore hcf applications in solving maximum equal distribution problems, including bundles of pens and pencils, equal class sizes, fruit rows, and livestock flocks.

this lecture explains that for two numbers, the product equals the product of their lcm and hcf, with a=gx and b=gy where x and y are coprime, unlike three-number cases.

Solve two-number problems using sum, difference, and product while applying LTM and HCF to identify valid pairs.

Learn to compute hcf and lcm from numbers and ratios, using elimination and division to find common factors. Apply these techniques to solve ratio problems and determine corresponding numbers.

Solve basic problems in simple interest by determining principal, rate, and time from given data, including six months at four percent per annum and related calculations.

Explore practical simple interest problems, converting days to years, calculating rate and principal from given periods, and combining multiple loans to solve for total interest in competitive examinations.

learn simple interest concepts using principal, rate, and time with deposits and loans, and compute final sum or time from A = P(1 + rt/100).

Learn how simple interest relates to principal and time via a five-year example. Solve rate questions using eight percent and other rates.

Explore the simple interest difference across three cases, deriving the SI difference from principal, rate, and time, with practical examples and problem-solving strategies.

this lecture teaches solving simple interest and ratios, including dividing a sum into 5% and 8% parts for a 3-year interest, and equal-interest investments across three schemes with different rates.

Explore the basics of compound interest, define interest on interest, and compare annual, half-year, quarterly, and monthly compounding, deriving the final sum formula P(1+R/100)^n and the compound interest relation.

Solve compound interest problems with annual compounding by applying final sum equals principal times (1 + r/100)^t to determine rate, time, and principal.

Explore half yearly, quarterly, and monthly compound interest calculations with practical examples, deriving final sums for given principal, rate, and time.

Solve quarterly compounded interest problems: compute the 16,000 rupee principal over nine months at 20% per annum, and determine the time for 3,200 rupees at 10% to reach 3,362.

Learn to compute compound interest with different annual rates by applying yearly growth factors and multiplying them, then subtract the principal to obtain the final amount of interest.

calculate the rate of interest from time duration differences under compound interest, with annual, semiannual, or quarterly compounding, using examples with two borrowers and varying time gaps.

Learn how compound interest relates to simple interest over two years, derive the key formula, and solve practice problems with annual rates to compare CI and SI.

Explore the difference between compound and simple interest and master a two-year shortcut to compute CI minus SI using simple interest, with six-month and yearly compounding examples.

Compute the difference between compound and simple interest to find the principal. Apply the simple interest and compound interest formulas for annual and semiannual compounding.

Explore the concept of percentage, its core formula, and eight practical models from basic to growth, including applications in competition, mixtures, geometry, and profit and loss.

Learn to compute percentage change using the reference value with examples: price increases from 6 to 7.5 (25% increase) and exam scores from 40 to 32 (20% decrease).

Master how to compute net and effective percentage changes from successive adjustments using rule three, with price and sales example problems.

explains a two-value model where value one is x percent more than value two and value two is y percent less than value one, then defines a rule to simplify these percentage problems.

learn to solve percentage less than or more than a third number problems by assuming the third number as 100 and using 100−X and 100−Y to compute their ratio.

Explore percentage-based exam problems by determining maximum marks, cutoff, and pass marks using percentage calculations and a shortcut formula, with examples at 20, 30, and 40 percent.

Explore growth rate models by applying a 10 percent per annum increase to population over two years, and learn rule nine formulas for increasing and decreasing values.

Develop skills in depreciation and growth rate problems by computing year-by-year percentage decreases and increases, including present value and population growth scenarios.

Explains solving percentage problems using a rule for two numbers less than a third number, expressing the first as a percentage of the second with (100−X)/(100−Y) × 100, plus examples.

Define selling price, cost price, profit, and loss, then apply percentage profit and percentage loss formulas. Use mobile phone and laptop examples to illustrate profit and loss calculations.

Compute profit percentages and cost prices from given selling prices, cost price, and repairs in basic problems, illustrating the relationship among cost price, selling price, and profit.

Master profit and loss problems by treating cost price as a hundred, and derive selling price or cost price from given profit or loss percentages.

Compute selling price and cost price from profit and loss percentages, using the standard formula and the direct method as a shortcut for SP and CP calculations.

Explore model two, where the cost price of x items equals the selling price of y items, and compute profit or loss percentages from cost price and selling price.

Explain how to calculate the effective profit or loss percentage from two successive sales, covering four cases and using three participants to illustrate cost price and selling price.

Explore problems on two successive sales, calculating effective profit percentage across buying and selling, and analyze price reductions and quantity changes to determine cost and selling prices.

Explore a model where two items sell at the same price, one at profit x% and the other at loss x%, showing the overall loss is x^2/100 percent.

Learn to compute cost price when selling price changes produce profit or loss, deriving cost price formulas from selling price adjustments and percent changes with four cases and examples.

Explore model 7: relate x items at CP and y items at SP to compute percentage profit or loss using cross multiplication and a shortcut formula.

Explore the basic definitions of ratios and proportions, and learn to express, compare, and compute inverse, duplicate, and compound ratios as fractions through practical examples.

Define proportion as the equality relation between two ratios. Show that product of means equals product of extremes, and explain directly proportional and inversely proportional with a constant of proportionality.

Explore the componendo-dividendo rule in proportions, examining interchanging mean terms, inverse tendo, and deriving equivalent expressions to simplify ratios.

Apply the componendo-dividendo rule to simplify ratios and solve problems using direct, dyadic, and dividend approaches. Demonstrations cover transforming expressions, solving for variables, and computing values such as (5X+3)/(X-2).

Explore main, mean proportional, and first to fourth proportions, using cross multiplication and the product of extremes equals the product of means to solve for x.

Explore expressions on two proportions by manipulating ratios such as a/b = x/y and b/c = p/q, showing how the product of numerators and denominators yields equivalent expressions.

solve two proportions problems using cross-multiplication and reciprocals. relate ratios by the product of numerators and denominators across multiple cases.

Learn to handle three proportions by using cross-multiplication and the product of numerators and denominators to derive the ratio a:b:c.

Explore problems on three and more than three proportions by forming expressions, multiplying across ratios, canceling terms, and simplifying fractions to derive A:B:C:D.

Explore ratio-based word problems in quantitative aptitude, solving distributions of money, marks, sweets, and numbers by using shares, fractions, and proportion.

Learn how to distribute a total amount among three people in a ratio L:M:N, derive each share and the pairwise differences using direct expressions.

Master ratio-based money distribution among three or more people by deriving A:B:C and B:C from given ratios and totals, and compute each person's share using proportional reasoning.

Explains a two-person income and expenditure model with a given income to expenditure ratio and savings, and derives incomes and expenditures using a simple cross-multiplication method.

Explore solving money management problems by using income and expenditure ratios, savings, and cross-product methods to determine incomes and expenditures in rupees.

explains solving age and ratio problems by deriving present ages from given present age ratios and after or before event ratios, using cross multiplication and a simple observation.

This lecture solves problems on ages in ratios and proportions, calculating present ages from past and future ratios, using stepwise techniques.

Learn to make four numbers A, B, C, D proportional by adding or subtracting a common value X to each term, with X computed from the given values.

Define mixture as two or more items joined, with two types: different items and same items. Use the rule of allegation to obtain the ratio using X, Y, Z.

Explore basic ratio and rule of allegation problems used to mix two items to reach a target price, with rice and alloy examples.

Apply the rule of alligation to solve mixture problems, using milk and water in vessels A and B to form a 1:1 mix and blend wine–water to equalize quantities.

Apply the rule of alligation to solve dilution and concentration problems, including 80% acid to 60%, 70% alcohol to 85%, and 80% gold to 95%.

Master ratios and proportions through practical mixture problems, from brass blends to spirit and water. Apply calculations in cases, kilograms, liters, and percentages.

Master percent concentration and dilution in mixtures for competitive examinations with three example problems: sand percentage after evaporation, sugar concentration after adding water, and milk percentage after adding milk.

Master mixture problems by computing cost price, selling price, and profit for blends of two items, and determine profit percentage in milk and petrol scenarios.

Explore how repeated replacements and dilutions affect the concentration of liquids a and b, using stepwise replacements, concentration formulas, and practical examples.

Learn how to compute the milk-to-water ratio when mixing two or more equal vessels by summing fractions and simplifying using ratios and least common multiple.

Compute work per person per day and per hour, derive efficiency, and apply to multi-person scenarios to solve unit work and double the work problems.

Explore work and time problems by dividing the work into two parts and calculating efficiency. Determine the number of workers and days required to complete the given units of work.

Study how three painters A, B, and C with times X, Y, and Z determine work completion when together or in pairs, using work and efficiency methods.

Analyze combined and individual work rates for three workers A, B, and C, deriving total work and times to finish a task when working together or alone.

Learn to solve two persons working together and alone problems using work rates, time, and efficiency to determine how long they finish a task.

Analyze work rate problems with three workers, calculating individual and paired efficiencies from given times, to determine how long A, B, and C take alone or together.

Three people A, B, and C have individual times of 24, 6, and 12 days; their combined rate sums to 7/24, so they finish in 24/7 days.

Explore problems where two or three workers join or leave midway, compute total work and individual efficiencies, and determine remaining days to finish the task using joint-work methods.

Learn to solve work-rate problems by modeling three workers with given times, compute individual and combined efficiencies, and find total days when workers join or depart.

Solve advanced work and time problems by analyzing individual and combined efficiencies, calculating total work, and determining days to complete tasks.

Learn to apply work and time efficiency to allocate compensation among collaborators, solving multi-person work problems and determining individual shares using rate-based calculations.

Explore work and efficiency problems, derive single-person times from relative efficiencies, and solve together-work cases for two or more people using efficiency relationships, with examples like Aisha, Barbu, and Bombo.

Analyze work-rate problems by comparing individual efficiencies, using ratio analysis and reciprocal daily work to determine how many days three or more workers take to finish a task.

Apply the time and work model to a two-pipe cistern system with two inlets and an outlet, to determine fill or empty times when pipes run alone or together.

Apply time and work concepts to pipe and pump problems, calculating individual and combined fill rates to determine how long tanks fill when pumps or taps operate together.

Solve time-based work problems in quantitative aptitude for competitive examinations using pipe fill rates, individual and combined efficiencies, and completion times.

Solve three-tap tank problems with A, B, and C (12, 15, 20 hours), using a 60-part capacity to derive rates and determine fill times for various openings.

Explore three-pipe system problems with two inlets and one outlet, including scenarios of three pipes running together to fill or empty the tank.

Compute net fill rates for inlet and outlet taps, determine the time to fill half the tank, and solve multi-pipe problems using the least common multiple to find individual efficiencies.

Solve tank filling and draining problems by treating the pump as an inlet and the leak as an outlet, applying work-rate methods to determine fill time, drain time, and capacity.