Math Ratio and Proportion for CAT and Other Competitive Exam

Learn the concept of continued ratio and two basic methods to compute it: aligning ratios by multiplying corresponding parts and using a lcm-based approach to equalize values.

Explore the continued ratio using a single line method to solve ratio questions quickly by scaling the first and last terms to equalize a to c, and solve verbally.

Learn the one-line method for continued ratio problems, applying it to p:q = 9:11 and q:r = 13:15 to obtain p:r as 117:165 and identify the middle term 143.

Apply the continued ratio one-line method to a three-ratio question and multiply the first terms to obtain the last. Use the lcm to balance all three ratios and find p:q:r.

Explore how to handle continued fractional ratios such as 1.2, 1.3, and 1.5 by choosing a common multiplier and multiplying all parts of the ratio.

Master continued ratio and simply fractional ratio problems by applying the lcm method to convert terms to integers, and know when ignoring the denominator is not appropriate.

Master the continued ratio and fractional ratio simplification methodology for competitive exams. Apply the ignore-and-multiply shortcut for integral values to quickly compute ratio values.

Solve a continued ratio word problem by setting three shares in a 2:3:5 relationship, then scale to total 93, revealing youngest, middle, and eldest allocations and the highest share.

Learn the fundamental rule for age-based problems: treat today as zero on a number line, with past to the left and future to the right.

Apply the sum of ages with a 4:7 ratio to find Billy at 16 and the child at 28, then Akhil is 32 and five years back 27.

This lecture analyzes an age-based problem using A:B ratios, differences with C, and a prime D between A and B to deduce C-D differences of seven or fourteen.

Apply ago and percentage concepts to age based problems, translating ten years ago and years hence to establish the Adam and Parker age ratio and Parker's age after nine years.

Use the number line to solve age based problems with a father and son in ratio 7x:2x, determine today’s ages, and find the father's age seven years back (40).

Explore the ratio concept using a stick split into two parts, where bigger:smaller equals whole:bigger. Rewrite ratios as 1:(y/x) or (x/y):1 and solve x^2+x-1=0 to get x.

Explore how ratio, percentage, and averages unite to solve a combined average problem, showing step-by-step calculation and arriving at a final answer of 200.

Explore a direct method to solve a ratio and percentage average problem, using A and B with marks in a 6:5 ratio and a combined average of 68.75%.

Learn the best method to tackle ratio, percentage, and averages in competitive exams, linking ratio concepts to percentage calculations and averages to compute totals and individual scores.

Tackling a word-based continued ratio problem for three workers, the lecture shows deriving A:B:C and scaling to the total.

Examine the continued ratio concept through a salary problem with two salaries in ratio 4:7, each increased by 25, and apply cross-multiplication and parts logic to find the initial salaries.

Apply a one-variable method to a two-variable income–expenditure problem: set incomes as 5x and 4x, compute expenditures from saving of one-third, and derive the saving ratio.

Apply the continued ratio method to solve salary, expenditure, and saving problems without variables, using a three-step approach to keep results integral, illustrated with salaries 15000 and 12000.

Explore ratio and distribution problems with two variables, solving simultaneous equations from apples and boys to determine totals and verify via cross-check.

Explore solving a distribution problem with apples and boys using a single variable, highlighting methods to find the number of apples and boys, and contrasting with two-variable approaches.

Explore ratios distribution with three coin types, ₹1, ₹0.50, and ₹0.25, where counts are in the ratio 2.5:3:4 and a total of ₹210 determines the number of ₹1 coins.

Apply ratio-based distribution to five subjects with ratios 10:9:8:7:6 to compute total marks, average, and passing status; four subjects exceed the 50% threshold.

Learn how to solve a ratio distribution based marks problem using arithmetic progression to determine how many subjects meet the 50% threshold without using variables, and connect ratios to algebra.

Explore degree and power concepts in ratio problems, defining power as the exponent and degree as the minimum power, and explain solvability when numerator and denominator degrees match.

Discover how to compare degrees in numerators and denominators and solve ratio-based expressions using a basic method, with a preview of a degree-based approach for easier questions.

Explore degree and power concepts to solve ratio-based problems, identify the degree as the minimum exponent, apply the degree zero condition, and substitute values to reach the answer.

The lecture explains why degree-based ratio questions cannot be determined when the highest powers in the numerator and denominator differ, demonstrated by substituting values and a parameter to reveal dependence.

Explore degree-based ratio problems and power concepts, noting that equal powers can still lead to cannot be determined when numerators and denominators involve different variables.

Explore degree-based ratio problems by cross multiplying cubic expressions to relate x and y, derive x^3 = y^3, and identify two solution scenarios.

Examine ratios with simultaneous equations by solving a problem that adds the same value to both terms to achieve a target ratio, and determine k.

Learn a ratio-based method to solve two equations with three variables by testing options to determine X:Y:Z, verifying each candidate against both equations.

Explain a ratios and equations problem by adding the same value to a and b to reach the ratio x/y, and derive k = (bx - ay)/(y - x).

Explore proper and improper fractions, their ratio properties, and how adding the same number to both numerator and denominator changes value, with applications to proportion.

Understand how ratios relate to proportions by comparing class gender ratios and corresponding party allocations, recognizing when two ratios are in proportion and when they are not.

Explains types of proportions in ratios, determines when two ratios are in proportion, and applies the product of means equals product of extremes to solve first through fourth proportions.

Explore types of proportions in ratio problems for cat and other competitive exams, including third, mean, and full proportion, with examples using 3, 8, and 10 to illustrate products.

Learn to solve two-value proportions by using the mean proportion to find the third or fourth term; the mean's square equals the product of the extremes.

Explore the formula of proportion and learn that when several ratios are in proportion, adding or subtracting numerators and denominators preserves the proportion.

Explore the second formula of proportion, including inverse ratios, alternate term interchange, and component and dividend properties.

Explains solving a proportion-based question by testing values and using elimination to verify expressions like (E^2 + B^2)/(C^2 + B^2), illustrating the best variable-based method.

This video demonstrates solving a proportion problem using the basic method: set A:B = C:D, express A and B in terms of each other, and obtain the answer B/(CD).

Explore how ratios and proportions apply to mixtures, learn base ratio concepts, and connect averages and percentages to solve related questions.

Learn ratio and mixtures through a water and milk problem, equalizing vessel quantities and applying the allegation method to determine the final water to milk ratio.

Learn to solve mixture ratio problems by equalizing totals (using the least common multiple), then multiply water and milk by the same factor to reach the desired ratio.

Solve mixture ratio problems by using the contents of two vessels containing water and milk, equalize totals, apply cross-multiplication to achieve the target ratio, and cross-check.

this lecture explains a ratio and proportion mix: equal quantities from two vessels with alcohol and water, yielding a final water to alcohol ratio of 43:17 and 28.33% alcohol.

Explains a ratio and proportion mixtures problem where a final ratio is given for wine and water, mixing them to obtain equal quantities, and notes elimination as a better method.

Learn to solve ratio and proportion mixtures problems involving wine and water, recognizing when initial ratios already match, and compute the final wine percentage from a combined solution.

Learn to find the mixing ratio that yields a 17:8 final mixture of wine and water, using ratio properties, cross-multiplication, and converting fractional ratios to whole numbers.

Learn the difference between simple average and weighted average. Use frequency to form weighted sums and derive the weighted-average formula through practical examples.

Explore alligation as a weighted-average allocation method for mixing two price categories to achieve a target cost, using the formula of subtracting values and pairing quantities.

Link the elimination formula with weighted average by converting it into alligation to solve ratio and proportion questions.

Apply the alligation method to solve wine and water mixture questions, converting ratios to a common base and deriving the final mixture ratio, such as 17:8.

Apply the alligation method to water-based mixture questions, using a common denominator to simplify calculations. Derive the mixing ratio of 1:4 to achieve the desired water balance in the mixture.

Apply the alligation method to a milk and water mix to derive the final ratio 13:12 and compare it to the ratio method, noting denominators should not be simplified.

Explore solving mixture problems by the allegation method and the method of ratios, compare approaches for milk and water scenarios, and apply proportion to balance totals.

Explore when to apply the allegation (elimination) method versus the mixture method for ratio problems, with a 85% and 100% milk example yielding 94% milk in a 2:3 ratio.

Apply alligation to mixture problems using fraction or percentage, illustrated with milk and water ratios. Compare the percentage base method and the allocation method for quick, exam-focused solutions.

Explore alligation and weighted average methods for mixture problems, using a 71% and 63% milk example in a 3:5 ratio to illustrate key concepts in ratio and proportion.

Apply the mixtures method to compute milk percentage from milk and water mixtures and totals. Conclude with 66% milk, linking to the weighted average (allegation) method.

Master the balancing method for mixture and ratio problems, compute deviations and total value from percentages, and compare it with other approaches to find the correct answer.