Paper I · 9 Logical Reasoning & Analytical Ability · APPSC Paper I
9.5 Time, work, speed and distance notes
9 notes, in reading order.
- 9.5.1Time and work: LCM method, efficiency and wages
Take the total work as the LCM of the given days, turn each worker into "units per day", and most time-and-work questions become simple division; when people, hours and work all change, use M₁D₁H₁/W₁ = M₂D₂H₂/W₂.
Standard · 8 min · Full course - 9.5.2Pipes and cisterns
Pipes and cisterns is time and work with a sign: inlets add to the tank, outlets and leaks subtract, and the tank fills (or empties) at the net rate.
Standard · 7 min · Full course - 9.5.3Speed, distance and time: average speed and relative speed
Distance = speed × time; most questions add one of three ideas: average speed = total distance ÷ total time, relative speed (subtract for the same direction, add for opposite directions), and for a fixed distance, time is inversely proportional to speed.
Standard · 8 min · Full course - 9.5.4Problems on trains
A train is not a point: to pass something it must cover its own length plus the length of the object, at the relative speed between them.
Standard · 7 min · Full course - 9.5.5Boats and streams
A stream adds to a boat's speed going down and subtracts going up, so downstream = B + S and upstream = B − S; half their sum is the boat's speed and half their difference is the stream's.
Standard · 7 min · Full course - 9.5.6Time and work: alternate days, leaving and joining, and men–women–boys equivalence
Break the job into phases, write the work done in each phase as rate × days, and make the phases add up to the whole job; for mixed groups, first turn everyone into one kind of worker.
Standard · 8 min · Full course - 9.5.7Races and games of skill: start, beat, dead heat and points
In the time the winner covers the full course, the loser covers the course minus the lead, so every race statement is a speed ratio; chain races by multiplying these ratios, never by adding the leads.
Standard · 6 min · Full course - 9.5.8Circular tracks: meeting points and first meeting at the start
On a circular track, two runners meet anywhere each time the faster gains (or, running opposite ways, together they cover) one full lap, and they meet at the start only at the LCM of their lap times.
Standard · 7 min · Full course - 9.5.9Speed problems: late and early arrival, stoppages and chases
Late-and-early questions are one distance at two speeds with a known time gap; stoppage questions are the distance lost per hour; chases are gap ÷ relative speed.
Standard · 7 min · Full course
Practise Time, work, speed and distance. Questions with answers explained, from the same topics.
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