How to Master Time, Speed, and Distance for CAT 2025

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.

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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

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