Want to know the importance of shortcuts and key applications in Time, Speed, and Distance for CAT? Well, being well-versed with shortcuts in TSD in the QA section of the CAT 2025 exam will help you in saving your time to a great extent by enabling you to apply formulas rapidly, interpret and solve problems efficiently, and make smart calculations. To maximize your scores in this section, solve the questions that are easier to tackle first, master mental math and approximation techniques, strengthen your knowledge of multiplication tables, squares, cubes, and other algebraic identities.
Also Read:
| CAT 2025 Quant Formula PDF Download |
|---|
Shortcuts and Key Applications of Time, Speed, and Distance for CAT
Time, Speed, and Distance problems are primarily based on the following concepts:
- Problems with two different speeds, i.e. when an individual covers equal distances but with different speeds (since the distance is constant, the average speed shortcut must be used)
- Average Time required for equal distances
- Problems based on Circular Track Meetings, where the concept of LCM (Least Common Multiple) of times for first meeting must be applied
- Train and Boat problems, where sum/difference of lengths and speeds must be directly used to obtain the required time
- Chasing Problems/Races, where the concept of relative speed must be used based on directions
- Integrated word problems, where time, speed, distance are combined with Work & Time, trains, and boats
Shortcut Formulas for Time, Speed, and Distance for CAT
Speed is inversely proportional to time and directly proportional to distance. Hence,
Distance = Speed x Time
Time = Distance
Speed
Average Speed = (Total distance travelled) / (Total time taken)
- Average speed = d1 + d2 + d3⋯dn
t1 + t2 + t3⋯tn
Average Speed (equal distance) = 2xy
x+y
where x, y are different speeds over equal distances
If the distance travelled is constant, and x and y are the two speeds at which the same distance has been travelled or covered,
Average speed = 2xy
x+y
When the time taken is constant, and x and y are the two speeds at which one has covered the distance at the same amount of time
Average speed = (x + y)
2
When the first part of any given distance is covered at a rate of v1 in Time t1 and the second part of the distance is covered at a rate v2 in Time t2, then the average speed is given by the following formula:
Average speed =
(v
1
t
1
+ v
2
t
2
)
t
1
+t
2
Inverse Proportionality of Speed & Time
- When the Distance (D) is Constant, Speed (S) and Time (T) are inversely proportional to each other.
- When Distance (D) is Constant, S is inversely proportional to 1/T.
- If the Speeds are in the ratio m:n, the Time taken will be in the ratio n:m.
Train Problems
-
Time Required to cross a pole =
Length of train
Speed -
Time Required to Cross Another Train (Same Direction) =
Sum of lengths
Speed difference -
Time Required to Cross Another Train (Opposite Direction) =
Sum of lengths
Speed sum
If two passenger trains are moving in the opposite direction, and the speed of one train is X km per hour and the speed of the other one is Y kilometre per hour, their relative speed is given by the following formula:
Relative speed = X + Y
Time taken by the trains in crossing each other is given by the following formula:
Time taken=
L
1
+L
2
X+Y
Where, L1 & L2 are the lengths of the trains respectively.
On the other hand, if the two trains are travelling in the same direction, and the speed of one train is X km per hour and the speed of the other one is Y kilometre per hour, their relative speed is given by the following formula:
Relative speed = X - Y
Time taken by the trains in crossing each other is given by the following formula:
Time taken=
L
1
+L
2
X-Y
Where, L1 & L2 are the lengths of the trains respectively.
Boats and Stream
- Speed downstream = Speed in still water + Speed of stream
- Speed upstream = Speed in still water – Speed of stream
If the ratio of the speeds of P and Q is p: q,
To reach the same distance, Time required by P : Time Required by Q = 1/p:1/q or q: p
Other Shortcut TSD Formulas for CAT
Two individuals or automobiles or trains start travelling in the opposing direction towards each other from two points, A and B, at the exact time. After they have crossed each other they take time a and b respectively to complete the journey. Find the speed ratio.
Speed of first =√b/a
Speed of second
Two individuals will cover the same distance and travel in opposite directions with two different speeds x and y. Where the total time is given, the Distance can be derived using the following formula:
Distance = xy × Total Time
x+y
Related Articles:
| Importance of CAT 2025 Mock Test During Preparation | |
|---|---|
| How to Improve Mock Test Score for CAT 2025? |
Please write to us on the CollegeDekho QnA Zone for further queries or apply through the Common Application Form (CAF) or call our helpline number 1800-572-9877 for assistance with admission to MBA colleges accepting CAT.
Are you feeling lost and unsure about what career path to take after completing 12th standard?
Say goodbye to confusion and hello to a bright future!
Was this article helpful?
Similar Articles
Tips to Reduce Exam Anxiety in CAT VARC Section
CAT Predicted Question Paper 2025: Important Topics, Chapters, Analysis
IIM Shortlist 2026: Check Results, Personal Interview, Dates, Cutoff, Seats, Selection Process
BHU MBA Admission 2026: Important Dates, Fees, Eligibility, Application Process, Selection Criteria, Cutoff and More
Smart Time Management Tips for Busy CAT Aspirants
Your 30-Day Foundation Plan for CAT 2025 Preparation