Time, Speed & Distance (TSD) - CAT Preparation
Question
What is the fundamental relationship between time, speed, and distance expressed in its most basic formula?Answer
Distance = Speed × Time. This is the core equation from which all other TSD relationships are derived.Question
If speed is doubled while time remains constant, what happens to the distance covered?Answer
Distance doubles. This demonstrates the direct proportionality between speed and distance when time is constant.Question
How is relative speed calculated for two objects moving in opposite directions?Answer
Relative speed = Speed₁ + Speed₂. Their speeds add up because they are closing the gap between them.Question
How is relative speed calculated for two objects moving in the same direction?Answer
Relative speed = |Speed₁ - Speed₂|. It is the absolute difference, representing the rate at which the gap between them changes.Question
In boats and streams problems, what is the formula for the speed of the boat in still water given its upstream and downstream speeds?Answer
Speed in still water = (Downstream Speed + Upstream Speed) / 2. This averages out the effect of the stream's current.Question
How do you calculate the speed of the stream in a boats and streams problem?Answer
Speed of stream = (Downstream Speed - Upstream Speed) / 2. This isolates the current's contribution to the boat's speed.Question
On a circular track, if two runners start from the same point and run in the same direction, when do they meet for the first time?Answer
They meet when the faster runner gains one full lap on the slower runner. The time is Track Length / Relative Speed (difference).Question
On a circular track, if two runners start from the same point and run in opposite directions, when do they meet for the first time?Answer
They meet when the sum of the distances covered equals the track length. The time is Track Length / Relative Speed (sum).Question
What is the correct method to calculate average speed for a journey with multiple parts?Answer
Average Speed = Total Distance / Total Time. You must calculate the time for each segment individually before summing.Question
Why is it incorrect to simply average the speeds of different journey segments to find the overall average speed?Answer
Because average speed is a weighted harmonic mean based on time, not a simple arithmetic mean. It depends on the time spent at each speed.Question
When a train crosses a pole (a stationary object with negligible length), what distance does it cover?Answer
The train covers a distance equal to its own length. Time taken = (Length of Train) / (Speed of Train).Question
When a train crosses a platform, what total distance must it cover?Answer
It must cover the sum of its own length and the length of the platform. Time = (Train Length + Platform Length) / Speed.Question
According to CAT strategy, what type of TSD questions are considered 'low-hanging fruit' and should be attempted first?Answer
Questions involving direct formula application (Average Speed, Relative Speed), simple boats & streams, or train lengths.Question
What is a key time-saving mental math conversion to remember for TSD problems?Answer
To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.Question
What is the recommended time allocation per TSD question in the CAT exam?Answer
Aim for 1.5 to 2.5 minutes per question. Use strategies like backsolving from options or approximation to save time.Shared with czed · AI-powered exam prep