Quantitative Aptitude - From Scratch to Advanced

Explore time and work concepts, solving problems for individuals and groups, focusing on efficiency, completion time, ratios of work, and wage allocation.

Learn how time and work problems use daily work rates to compute completion time, compare efficiencies, and allocate wages by each member’s contribution.

calculate the time for a man, his father, and his son to finish a job together by summing their daily work rates and taking the reciprocal.

Solve a three-person work-rate problem using A, B, and C with A+B=72 days, B+C=120 days, and C alone 90 days to find all three’s completion time.

Calculate a work-rate problem where two workers can finish in 18 and 15 days; after 10 days, determine the remaining work and the time needed for completion.

discover a shortcut for solving leaving based problems by using one day work rate and simple equations to determine total days required.

Set hourly work rates for man, woman, and boy, form equations from group combinations, and solve for x, y, z to determine how many hours or days complete the work.

Learn to analyze pipe flow problems with pipes a and b, calculating fill and empty rates and determining tank time by combining rates.

Explore solving a three-source work problem with a leaving equation, where A and B run five minutes before C joins, to find the remaining work.

Identify a straightforward approach to a three-valve filling problem with A, B, and C, and determine tank fill times using alternating operations and given percentages.

Tackle a two-pipe tank filling problem by running both pipes for x minutes, then turning off one pipe to finish within 30 minutes, using rate equations to find x.

Explore time and distance concepts by applying speed = distance divided by time, convert between units such as km/h and m/s, and calculate average speed across different speeds.

Apply speed equals distance divided by time to solve basic problems, then convert all speeds to a common unit to compare them accurately.

Apply the time = distance divided by speed formula to a perimeter problem, summing field segments to get total distance and converting units to keep consistency.

Determine the speed ratio of a cyclist and a jogger when the jogger covers half the distance in double the time, and emphasize capturing information and mapping to solve.

Explore a non uniform speed problem where the journey’s first half runs at 21 km/h and the second half at 24 km/h for a total distance of 24 km.

Apply a quick trick for bus stopping problems by comparing non-stop and stopped speeds; divide the speed difference by the original speed to get stop time in minutes.

solve a time-difference walking problem by comparing two speeds, 3 km/h and 3.7 km/h, with a 0.5 hour arrival gap to determine the travel distance.

Learn to apply time and distance concepts to trains, calculating speed, distance, and crossing times using train length, platform length, and relative speed for opposite and same-direction scenarios.

Master time and distance problems using a formulae based approach, solving train crossing scenarios, unit conversions, and cross-bridge calculations.

Apply relative-speed concepts to crossing a tunnel and opposite-direction trains, using the total distance (train length plus tunnel length) and converting between m/s and km/h to find speeds.

Two trains of equal length run in the same direction at 46 km/h and 30 km/h; they cross in 36 seconds, so each train is 50 meters long.

Solve a two-trains crossing problem in opposite directions with lengths 100 m and 200 m; one train runs at 120 km/h, yielding about 111 km/h for the other.

Solve a train overtakes two pedestrians walking in the same direction at 2 km/h and 4 km/h using 9 and 10 second crossings to find the length of 50 metre.

Learn to solve two trains crossing problems from different stations using a single relative-speed formula; infer speeds from travel times, assume 100 km distance, and calculate the crossing time.

Analyze a scenario where two trains meet en route, then reach their destinations in nine and six hours. Derive the speed ratio using the square-root relation of post-meeting times.

Explore boats and streams, covering upstream and downstream speeds, boat speed in still water, and how speeds relate, with upstream equals boat minus stream and downstream equals boat plus stream.

Solve downstream and upstream speed problems by applying velocity of the current concepts, compute the boat speed and current speed from distance and time.

Solve contextual river speed problems by finding the still-water boat speed and the upstream and downstream speeds from given stream velocity data.

Explore rate problems involving boats and currents, calculating downstream and upstream speeds using still water speed and current speed to solve for the unknown rate.

Compute downstream distance when a boat's still-water speed is 15 km/h and current speed is 3 km/h; downstream speed becomes 18 km/h, so a 12-minute trip covers 3.6 km.

Master the complete concept of percentages, including converting fractions to percent, base interpretation, and solving 'what percent of x' problems, with applications to price changes, population growth, and depreciation.

Compute what percent of x is y by using numerator over denominator and converting units, such as 7.2 kg to 18 grams.

Learn how to determine what percent x is of y by using numerator and denominator and converting the ratio to a percentage, with examples like 0.01 and 0.1.

Convert hours to a fraction of a 24-hour day and multiply by 100 to find the percent. For example, 3 hours equals 12.5% of a day.

Learn to find what percent of x percent is y percent by canceling the ratio, avoiding confusion, and seeing why the result comes out as 60 percent in the example.

Learn to solve percentage-based problems by defining larger and smaller numbers, translating statements like the difference equals 20 percent of the larger into equations, and solving.

Convert statements like 'X is 90 percent of white' into equations, substitute values, and cancel to find the required percent, clarifying numerator and denominator.

Derive a practical theorem from an abstract problem using percent calculations, explaining two percent and other percentages, and showing how to combine percentages to obtain results.

Apply De Morgan's theorems to a two-subject failure problem, using complement, union, and intersection to determine the percentage who failed and the total number of students.

Explore profit and loss concepts by comparing cost price, selling price, and calculating gain and loss, while applying key formulas for profit percent and loss percent.

Solve real-life profit and loss problems, determine greatest profit from buying books at 200–350 and selling at 302–425, and compute shopkeeper gains and profit percentages.

Compute cost price from selling price and gain, and determine gain percentage using the example: cost price 85 rupees, selling price 100 rupees, gain 15 rupees, yielding about 17.6%.

Learn to find the cost price when the selling price is 34.80 rupees after a 2% loss, yielding a cost around 35.50 rupees.

Learn to compute profit percent from the ratio of cost price to selling price, using gain, selling price, and cost relationships in ratio problems.

This lecture solves a businessman's stock problem by calculating the overall gain when one-third is sold at 20 percent and the rest at 14 percent, yielding 18 percent.

Learn the concepts of mixture and alligation, mix two commodities at given cost prices, and apply the alligation rule to determine the ratio that yields the mean price.

Explore problems 1–3 using the rule of alligation to find mixture ratios and cost prices when mixing substances like water with milk, and compute selling price and gain.

Demonstrate solving mixture problems with the rule of alligation, ratio analysis, and concentration concepts. Apply these methods to compute mean prices, quantities, and profits in blending spirits with water.

Count three-digit numbers from digits 2,3,5,6,7,9 that are divisible by 3 using permutation concepts with no repeated digits; emphasize that order matters in these counts.