Speed, Distance and Time: Placement Aptitude Test Guide

Speed, distance, and time problems appear in every campus placement aptitude test, from TCS NQT to AMCAT to company-specific assessments at Cognizant and Wipro.

They’re not conceptually hard. What separates candidates who clear the quantitative section from those who don’t is whether they can classify the question type in under 20 seconds and execute the right formula without rebuilding the method from scratch under pressure.

Why Motion Questions Appear in Every Placement Test

Aptitude test designers use speed-distance-time problems because they satisfy a strict requirement: the mathematical content is predictable (every student learned it in school), but the question variants are wide enough to measure procedural accuracy under time pressure.

Motion problems appear in TCS NQT, AMCAT, eLitmus, and Mercer Mettl tests. The questions cluster around four types:

• Basic speed-distance-time (find speed, distance, or time given the other two)
• Relative motion (two objects moving toward or away from each other)
• Average speed for a multi-leg journey
• Train or platform crossing problems

Average speed and relative motion are the two types that cause the most errors, not because students lack knowledge of the formulas, but because the instinctive wrong answer is close enough to the correct one to feel convincing.

Core Formulas and Unit Conversions

Three relationships govern every motion problem:

• Speed = Distance / Time
• Distance = Speed x Time
• Time = Distance / Speed

The standard placement test gives speed in km/h and asks about events measured in metres or seconds. The unit conversion is therefore an almost universal sub-step:

• To convert km/h to m/s: multiply by 5/18
• To convert m/s to km/h: multiply by 18/5
• Derivation: 1 km = 1000 m, 1 hour = 3600 s, so 1 km/h = 1000/3600 m/s = 5/18 m/s
• Example: 72 km/h = 72 x (5/18) = 20 m/s

Train and platform crossing problems require this conversion almost every time because train lengths appear in metres while speeds are given in km/h.

Relative Motion: Trains, Boats, and Platforms

Relative motion is the variant with the most trap answer choices and the one most students lose avoidable marks on.

Relative Speed Rules

• Opposite directions: relative speed = Speed1 + Speed2
• Same direction: relative speed = Speed1 minus Speed2 (take the positive value)

For train problems, the distance used depends on what is being crossed:

• Crossing a pole or a stationary person: distance = length of train only
• Crossing a platform or a bridge: distance = length of train + length of platform

The trap answer in a platform-crossing question is always the one computed using only the train’s length. Re-reading the last line of the question before starting eliminates this error every time.

Boat problems follow the same algebra with different labels:

• Downstream speed = boat speed in still water + current speed
• Upstream speed = boat speed in still water minus current speed

If the problem gives downstream and upstream speeds directly:

• Boat speed in still water = (downstream speed + upstream speed) / 2
• Current speed = (downstream speed minus upstream speed) / 2

Average Speed: The Formula Students Get Wrong

Average speed is the most misapplied formula in motion problems on campus tests. The instinct is to add the two speeds and halve the result. That instinct is wrong whenever the same distance is covered at two different speeds.

Average speed = Total distance / Total time

For equal-distance legs at speeds a and b, the algebra works out as:

• Total distance = 2d (two legs of distance d each)
• Total time = d/a + d/b = d(a + b) / (ab)
• Average speed = 2d / [d(a + b) / (ab)] = 2ab / (a + b)

This result is the harmonic mean of a and b. It is always less than or equal to the arithmetic mean. Worked Example 4 below shows the arithmetic with specific numbers and a verification step.

The formula inverts in one case: if equal time is spent at each speed rather than equal distance, the average speed is the arithmetic mean (a + b) / 2. Identify which condition the question states before choosing the formula.

Worked Examples

All examples below are derived from first principles and independently verified.

Example 1: Basic Speed-Distance-Time

• Given: A car travels 300 km in 5 hours.
• Find: Speed in km/h, then convert to m/s.
• Step 1: Speed = 300 / 5 = 60 km/h.
• Step 2: Convert to m/s: 60 x (5/18) = 300/18 = 50/3 m/s (approximately 16.67 m/s).
• Answer: 60 km/h or 50/3 m/s.

Example 2: Train Crossing a Platform

• Given: A train 150 m long travels at 90 km/h. A platform is 300 m long.
• Find: Time for the train to completely cross the platform.
• Step 1: Total distance = 150 + 300 = 450 m.
• Step 2: Convert speed: 90 x (5/18) = 25 m/s.
• Step 3: Time = 450 / 25 = 18 seconds.
• Answer: 18 seconds.
• Verification: 25 m/s x 18 s = 450 m = 150 + 300. Correct.

Example 3: Two Trains Moving Toward Each Other

• Given: Train A is 200 m long at 60 km/h. Train B is 300 m long at 40 km/h, moving toward A.
• Find: Time for the two trains to completely pass each other.
• Step 1: Total distance = 200 + 300 = 500 m.
• Step 2: Relative speed = 60 + 40 = 100 km/h. Convert: 100 x (5/18) = 500/18 m/s.
• Step 3: Time = 500 / (500/18) = 500 x (18/500) = 18 seconds.
• Answer: 18 seconds.

Example 4: Average Speed Trap

• Given: A bus travels from city A to city B at 60 km/h and returns at 40 km/h.
• Find: Average speed for the complete round trip.
• Step 1: Use 2ab/(a+b) since both legs cover equal distance.
• Step 2: Average speed = (2 x 60 x 40) / (60 + 40) = 4800 / 100 = 48 km/h.
• Answer: 48 km/h. Not 50 km/h.
• Verification: Say each leg = 120 km. Time A to B = 120/60 = 2 h. Time B to A = 120/40 = 3 h. Total time = 5 h. Average = 240 / 5 = 48 km/h. Correct.

Example 5: Boats and Streams

• Given: A boat travels 36 km downstream in 2 hours and 24 km upstream in 3 hours.
• Find: Boat speed in still water and current speed.
• Step 1: Downstream speed = 36 / 2 = 18 km/h.
• Step 2: Upstream speed = 24 / 3 = 8 km/h.
• Step 3: Boat speed = (18 + 8) / 2 = 13 km/h.
• Step 4: Current speed = (18 minus 8) / 2 = 5 km/h.
• Answer: Boat speed = 13 km/h. Current speed = 5 km/h.
• Verification: Downstream = 13 + 5 = 18 km/h. Upstream = 13 minus 5 = 8 km/h. Matches given data.

Example 6: Overtaking in the Same Direction

• Given: Train P is 180 m long at 72 km/h. Train Q is 120 m long at 54 km/h. Both travel in the same direction.
• Find: Time for train P to completely overtake train Q.
• Step 1: Total distance = 180 + 120 = 300 m.
• Step 2: Relative speed = 72 minus 54 = 18 km/h. Convert: 18 x (5/18) = 5 m/s.
• Step 3: Time = 300 / 5 = 60 seconds.
• Answer: 60 seconds.

Preparing Efficiently for Motion Questions

Campus aptitude tests allocate 2 to 4 questions to speed-distance-time and related topics. The return on preparation time is high because the question pool is narrow and the formulas are compact.

Practical approach for timed tests:

• Classify the type first. Basic, relative motion, average speed, or crossing problem? Correct classification takes 15 to 20 seconds and prevents wrong-formula errors that cost far more time to unwind.
• Convert units before substituting. Write the converted speed on scratch paper before plugging into the formula. Substituting km/h into a formula expecting m/s is the most common arithmetic error on this topic.
• For average speed questions: check whether the two segments cover equal distances or equal time. The formula differs for each case.
• Re-read the last sentence of crossing problems. “Cross a pole” and “cross a platform” require different distances. Using the wrong one is the trap answer.

IndiaBix Speed, Time and Distance has a question bank in the same format campus tests use, sorted by difficulty and with worked solutions. The TCS NQT careers page links to the official test format and sample preparation materials.

For the full picture of what the quantitative section covers beyond motion, the campus placement evaluation test guide maps every section with preparation timelines. Time and work problems use the same rate-decomposition logic as speed-distance problems. The time and work aptitude guide covers that topic with matching depth and verified examples. For analytics companies like Mu Sigma, where quantitative reasoning is weighted more heavily than at mass-hiring IT firms, the Mu Sigma MuApt analysis maps how motion-style reasoning appears in that context. The placement preparation books guide lists which standard titles cover motion and kinematics most clearly.

The classify-before-calculate habit that distinguishes strong aptitude performers from average ones is the same structured decomposition that makes AI tools genuinely useful rather than erratic. TinkerLLM, starting at ₹299, applies that same approach to real AI workflows, so the problem-solving instinct you build here transfers directly.