Math Tricks and Techniques For All Competitive Exams

Explore how ratios express part-to-part relationships and fractions express part-to-whole relationships using boys and girls in class examples, and learn why you cannot add ratios directly.

Divide a total value by a ratio, as shown with 3:4:5 and 24,000 to yield 6,000, 8,000, and 10,000, then combine ratios by equalizing terms.

Explore proportion as a relation between ratios, illustrated by $0.50 yielding ten chocolates and $0.70 yielding fourteen, and the rule that product of extremes equals product of means.

Learn to identify main, third, and fourth proportion, and distinguish direct and inverse proportion using speed-distance and heat-water level examples.

Learn how to define percentage, compute it as obtained value divided by total value multiplied by 100, and use it to compare scores with practical examples.

Compute percentage change using (new minus old) divided by old times 100, with 350 to 450 marks. Convert percentages to fractions by dividing by 100, and back to percentages.

Master practical percent calculations and shortcuts for competitive exams through examples like 20% of 600, 39% of 700, 250% of 300, and 20% of 40% of 350.

Learn percentage change from an initial value of 100x, tracing stepwise increases and decreases to final values, with mobile price and population examples.

Explore profit and loss by examining cost price, selling price, and market price. Learn to calculate profit, loss, and discount percentages.

Explore solving a discount–profit problem by linking cost price, selling price, and market price; with a 20% discount on a 600 mark price and 20% profit, cost price is 400.

Learn to compute profit or loss percentage from cost price and selling price in equal selling price two-mobile scenarios, including 25% profit, 5% profit, and a 20/21% loss.

Apply successive discounts of 30% and 40% to see the final price become 0.42 of the initial price; solve for the original price using a 100x baseline.

Explain the difference between simple interest and compound interest, showing simple interest on the principal and compound interest on accumulated interest, with examples of principal, rate, and time.

Explore how to compute averages for linear and non-linear data, using first plus last divided by two or middle values, with practical examples.

This lecture explains nonlinear data lacks inherent order and introduces weighted average, showing how to compute a class average using weights for boys, girls, and teachers, yielding 14.4 gauges.

Learn practical tricks for solving average problems using cricket scores and class weights, to quickly find missing values such as 70 runs and 51 kg.

Learn to solve mixture problems by combining equal quantities from two vessels with ratios 2:3 and 3:4 using a common multiple to obtain 29:41 milk to water ratio.

Explore algebraic expressions with variables and constants, and learn how operations form expressions like 3x + 4y + 3, then classify single-term, binomial, and trinomial forms.

Learn the near hundred square technique using base 100, where you add the difference from 100 and square that difference, keeping a two-digit second part with carries as needed.

Solve a set of example math questions, give each question a 15-second thinking interval, and practice applying math tricks and techniques for competitive exams.

Learn cubing techniques to compute the cubes of double-digit numbers using single-digit cubes, carry handling, and doubling the middle value with step-by-step examples.

Learn a cube root technique for numbers up to 200. Split the number into parts, locate the first part between cubes, and use the last digit to determine the root.

Discover two practical multiplication techniques: technique 1 uses unit digits summing to ten to split products, and technique 2 uses the numbers' distance from a hundred to simplify calculations.

Technique 7 uses a line-based, pictographic method to multiply numbers by drawing lines and counting intersections in three parts, with carry adjustments for two-digit middle parts.

Explore division techniques using the cushioned and remainder method to compute quotients and remainders through long-division steps, with practical examples for competitive exams.

Explore digital sum techniques to quickly find the single-digit result by adding digits and using elimination to simplify addition, subtraction, multiplication, division, percentages, and other simplifications.