Time, Speed, Distance, Boats and Trains Practice Questions for CAT: 173+ Solved Questions with Step-by-Step Solutions

Solve 173+ Time, Speed, Distance, Boats and Trains practice questions for CAT with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Time, Speed, Distance, Boats and Trains

↔

Chapter Journey

Time, Speed, Distance, Boats and Trains

Step 1 • 11 CAT PYQs • Importance 0.76

🚶 Linear Motion and Relative Speed

Master distance-speed-time, meetings, chases, speed changes, stoppages, and multi-person motion.

Step 2 • 2 CAT PYQs • Importance 0.30

🚣 Boats, Streams and Water Travel

Apply upstream-downstream logic using still-water speed and stream speed.

Step 3 • 3 CAT PYQs • Importance 0.35

🚆 Trains, Crossings and Track Problems

Handle train lengths, poles, platforms, and opposite-direction crossings.

Step 4 • 3 CAT PYQs • Importance 0.35

🕒 Clocks, Circular Motion and Escalators

Convert movement into relative angular speed or effective speed on moving platforms.

By the end of this chapter: you should be able to convert every motion story into distance covered, time taken, and speed used.

Linear Motion and Relative Speed

Arithmetic → Time, Speed, Distance, Boats and Trains → Topic 1

Linear Motion and Relative Speed

Motion questions become easy when you track who covers which distance in whose time.

D=ST

Basic distance-speed-time

Meeting and chasing

Speed-change equations

CAT relative-speed patterns

Time, Speed, Distance, Boats and Trains: Solved Questions with Step-by-Step Explanations (5 Problems)

Question 1 · Quantitative Ability MCQ

A car travels at a constant speed of $60$ km/h for $2.5$ hours. What is the total distance covered by the car in kilometers?

A.
120
B.
150
C.
180
D.
200

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct application of the fundamental distance formula, recognisable because speed and time are given, and distance is asked.

Step 1: Identify the given values. Speed $S = 60$ km/h, Time $T = 2.5$ hours.

Step 2: Use the formula $Distance = Speed \times Time$ .

Step 3: Calculate $D = 60 \times 2.5 = 150$ km.

Answer: 150

Question 2 · Quantitative Ability MCQ

The "Final CAT Checklist" helps you map problem statements to methods. If a question asks for the time when two runners starting together on a circular track meet for the first time anywhere on the track while running in the same direction, which method does the checklist prescribe?

A.
LCM of their individual lap times
B.
Track Length divided by Sum of Speeds
C.
Harmonic Mean of their lap times
D.
Track Length divided by Relative Speed (Difference)

Correct Answer:

Step-by-Step Solution

Key idea: This is a pattern recognition question, recognisable because it asks to match a specific circular motion scenario to its correct mathematical method.

Step 1: Analyze the conditions: "circular track", "same direction", and "meet anywhere" (not specifically at the start).

Step 2: Recall the rules for circular motion. Meeting at the starting point requires LCM of lap times. Meeting anywhere on the track requires relative speed.

Step 3: Since they run in the same direction, their relative speed is the difference of their speeds ( $S_{1} - S_{2}$ ).

Step 4: The time to meet for the first time anywhere is the Track Length divided by this Relative Speed.

Answer: Track Length divided by Relative Speed (Difference)

Question 3 · Quantitative Ability MCQ

You are solving a train problem involving two trains moving in the same direction. Train A ( $120$ m) moves at $90$ km/h. Train B ( $180$ m) moves at $72$ km/h. You need to find the time taken for them to completely cross each other.

According to the Final CAT Checklist decision tree, which immediate next step is strictly required before applying any time formula?

A.
Calculate relative speed as $90 + 72 = 162$ km/h
B.
Convert individual speeds to m/s, then subtract to find relative speed
C.
Add lengths $120 + 180 = 300$ m and divide by average speed
D.
Subtract speeds in km/h first, then convert the difference to m/s

Correct Answer:

Step-by-Step Solution

Key idea: This is a procedural decision question based on the Final Checklist. It tests optimization and workflow order, not just the final answer.

Step 1: Analyze the motion type.

Trains move in the SAME direction.

Checklist Rule: Relative Speed = Difference of speeds.

This eliminates Option A which adds speeds.

Step 2: Analyze unit requirements.

Lengths are in meters. Time is requested in seconds. Speeds are in km/h.

Conversion is mandatory.

Step 3: Evaluate conversion efficiency (The Checklist Layer).

Method 1 (Option B): Convert $90 \to 25$ m/s. Convert $72 \to 20$ m/s. Subtract: $25 - 20 = 5$ m/s. Two conversions, one subtraction.

Method 2 (Option D): Subtract in km/h first: $90 - 72 = 18$ km/h. Convert once: $18 \times \frac{5}{18} = 5$ m/s. One subtraction, one conversion.

Step 4: Apply Checklist Priority.

The checklist prioritizes minimizing operations to reduce error risk. Converting the difference is computationally superior and less prone to fraction errors than converting two separate larger numbers.

Therefore, Option D is the strict next best step per optimized protocol.

Step 5: Reject distractors.

Option C uses average speed, which is never valid for crossing time.

Answer: Option D.

Question 4 · Quantitative Ability MCQ

When visualizing clock hands as one hand chasing the other, at what relative rate does the minute hand close the angular gap on the hour hand?

A.
$6^{\circ}$ per minute
B.
$5. 5^{\circ}$ per minute
C.
$0. 5^{\circ}$ per minute
D.
$1 2^{\circ}$ per minute

Correct Answer:

Step-by-Step Solution

Key idea: this is a clock relative-speed question. The trigger is asking for the rate at which the minute hand "chases" or gains on the hour hand.

Step 1: Recall the individual speeds. The minute hand moves at $6^{\circ}$ per minute. The hour hand moves at $0. 5^{\circ}$ per minute.

Step 2: Find the relative speed. Since they move in the same direction, the minute hand gains on the hour hand at the difference of their speeds.

Step 3: Calculate the difference: $6^{\circ} - 0. 5^{\circ} = 5. 5^{\circ}$ per minute.

Answer: $5. 5^{\circ}$ per minute.

Question 5 · Quantitative Ability MCQ

Using the formula $D = \frac{S _{1} \times S _{2}}{∣ S _{1} - S _{2} ∣} \times Δ T$ for early/late problems, find the distance if the two speeds are $45$ km/h and $60$ km/h, and the total time difference $Δ T$ is $30$ minutes.

A.
90 km
B.
180 km
C.
360 km
D.
5400 km

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct formula substitution question, recognisable because it explicitly provides the early/late formula and asks for the distance.

Step 1: Identify the given values: $S_{1} = 45$ km/h, $S_{2} = 60$ km/h, and $Δ T = 30$ minutes.

Step 2: Ensure units are consistent. Since speeds are in km/h, convert $Δ T$ to hours: $30 minutes = 0.5 hours$ .

Step 3: Substitute into the formula: $D = \frac{45 \times 60}{∣45 - 60∣} \times 0.5$ .

Step 4: Calculate the denominator: $∣45 - 60∣ = ∣ - 15∣ = 15$ .

Step 5: Calculate the fraction: $\frac{2700}{15} = 180$ .

Step 6: Multiply by $Δ T$ : $180 \times 0.5 = 90$ km.

Answer: 90 km

A question from this chapter

Question 1

A car travels at a constant speed of 60 km/h for 2.5 hours. What is the total distance covered by the car in kilometers?

Question 2

The "Final CAT Checklist" helps you map problem statements to methods. If a question asks for the time when two runners starting together on a circular track meet for the first time anywhere on the track while running in the same direction, which method does the checklist prescribe?

Question 3

You are solving a train problem involving two trains moving in the same direction. Train A (120 m) moves at 90 km/h. Train B (180 m) moves at 72 km/h. You need to find the time taken for them to completely cross each other. According to the Final CAT Checklist decision tree, which immediate next step is strictly required before applying any time formula?

Question 4

When visualizing clock hands as one hand chasing the other, at what relative rate does the minute hand close the angular gap on the hour hand?

Question 5

Using the formula D = \frac{S _{1} \times S _{2}}{∣ S _{1} - S _{2} ∣} \times Δ T for early/late problems, find the distance if the two speeds are 45 km/h and 60 km/h, and the total time difference Δ T is 30 minutes.

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Time, Speed, Distance, Boats and Trains Practice Questions for CAT: 173+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Time, Speed, Distance, Boats and Trains

Time, Speed, Distance, Boats and Trains

🚶 Linear Motion and Relative Speed

🚣 Boats, Streams and Water Travel

🚆 Trains, Crossings and Track Problems

🕒 Clocks, Circular Motion and Escalators

Linear Motion and Relative Speed

Linear Motion and Relative Speed

Time, Speed, Distance, Boats and Trains: Solved Questions with Step-by-Step Explanations (5 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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