Duplicate Ratio
Square of the initial ratio terms.
Ratio = a^2 : b^2
Quantitative Aptitude
Divide values, compound ratios, identify mean/third/fourth proportionals, and apply Componendo-Dividendo logic without using complex algebra.
Ratios compare quantities of the same kind and are the glue between many aptitude topics: partnership, mixtures, ages, coins, and combined comparisons (A:B, B:C, C:D). Proportion problems reuse the same four operations: scaling a ratio to fit a total, compounding ratios, and finding missing terms (mean, third and fourth proportionals). Componendo-dividendo and the "add/subtract a constant to both terms" puzzles are the classic exam twists.
A ratio compares two values; a proportion states that two ratios are equal.
Square of the initial ratio terms.
Product of extremes equals product of means.
The recurring question patterns in this topic — know the shape of each pattern before you solve.
Split a quantity among parties proportionally to the ratio parts.
₹144 in 3:5 → smaller part 54.
Combine A:B, B:C, C:D into a single A:D ratio.
A:B = 2:3, B:C = 4:5, C:D = 6:7 → A:D = 16:35.
Both terms decrease by the same constant; new ratio given.
(3x−9):(5x−9) = 12:23 → numbers 33 and 55.
Find the missing term of a proportion.
Fourth proportional to 4, 9, 12 → 27.
Counts are in one ratio, values in another; reconcile via value per coin.
₹1:50p:25p in 5:6:8 → values 5x:3x:2x.
High-signal questions with full solution flow across difficulty patterns.
Classic exam problems worth internalizing — each one ships a complete step-by-step solution.
Line up A:B and B:C to find A:B:C by duplicating adjacent numbers.
Where most students lose marks — review these before you sit the test.
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