AiraAptitude

Calculate train lengths, relative speeds when passing stationary objects, platforms, and moving trains.

Solve problems involving uniform motion, average speed across variable journeys, and delay compensations.

Model inlet and outlet fill and drain rates, leakages, and simultaneous or alternating pipe operations.

Analyze upstream and downstream motion with river currents, swimmer speeds, and round-trip times.

Calculate headstarts, lead distances, time penalties, and winning margins in competitive track races.

Master percentage increases, population growth formulas, successive percentage changes, and exam passing score benchmarks.

Compute unitary work rates, multi-worker efficiencies, wage divisions, and workers joining or leaving midway.

Set up linear age equations across past, present, and future ratio conditions between family members.

Determine arithmetic means, weighted averages, batting and bowling stats, and corrected observation averages.

Solve direct and inverse proportions, compound ratios, third and fourth proportionals, and proportional splits.

Apply direct and indirect variation across multi-variable resource equations involving men, hours, days, and output.

Perform precise operations on pure and mixed recurring decimals, decimal places, and vulgar fraction conversions.

Quickly evaluate complex nested algebraic expressions using BODMAS rules and algebraic identities.

Calculate square roots and cube roots via prime factorization, division method, and surd simplification.

Calculate principal amounts, annual interest rates, tenure, and total amounts under linear interest accrual.

Evaluate exponential interest compounding across annual, half-yearly, and quarterly periods with CI - SI differences.

Determine profit margins, loss percentages, marked prices, successive discounts, and dishonest dealer weighing errors.

Apportion business profits and losses among partners based on proportional capital contributions and investment duration.

Find mixing ratios of commodities with different prices/concentrations, and liquid replacement iterations.

Calculate annual dividends, market values, yields, brokerage fees, and stock transactions across companies.

Determine the true discount and present worth of bills of exchange due at a future date at given interest rates.

Analyze banker's discount, banker's gain, true discount, and face value on bills of exchange.

Apply trigonometry to determine heights of towers, observer angles of elevation, and shadow lengths.

Compute 2D surface areas, perimeters, pathways, and diagonals for rectangles, squares, circles, and triangles.

Determine capacities and surface areas of 3D solids including cubes, cuboids, cylinders, cones, and spheres.

Calculate odd days across centuries, determine days of the week for historical dates, and find matching calendar years.

Determine angles between minute and hour hands, coincident times, right angles, and fast/slow clock corrections.

Identify prime numbers, divisibility tests, remainders, unit digit cyclicity, and digit arithmetic properties.

Compute Greatest Common Divisors, Lowest Common Multiples, and solve recurring bell and tile measurement problems.

Simplify fractional exponent powers, radical expressions, conjugate binomial surds, and exponential equations.

Apply product, quotient, and power laws of logarithms to simplify expressions and determine character/mantissa digits.

Recognize arithmetic, geometric, polynomial, and alternating numeric patterns to spot discrepancies.

Solve ordered arrangements (permutations) and unordered selections (combinations) with restrictions and repetitions.

Determine odds and probabilities for coin tosses, dice rolls, standard 52-card decks, and colored urn selections.