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Time and Distance

Practice MCQs

None

Quantitative Aptitude Time and Distance Competitive Exams

Time and Distance is one of the most important quantitative aptitude topics. It is based on the relationship between speed, distance, and time. Questions from this chapter appear frequently in banking exams, SSC, railways, police exams, entrance tests, and general aptitude exams.

What is Time and Distance?

Time and Distance questions deal with the movement of a person, vehicle, train, boat, cyclist, or any moving object. These questions are solved using the relationship between speed, distance, and time.

Speed tells how fast an object moves. Distance tells how far it travels. Time tells how long it takes to cover the distance.

Quick idea: If any two values among speed, distance, and time are known, the third value can be calculated.
Term Meaning Example
Speed Distance covered per unit time 60 km/h
Distance Total path covered by a moving object 120 km
Time Duration taken to cover the distance 2 hours
Average Speed Total distance divided by total time 240 km / 4 h = 60 km/h
Relative Speed Speed of one object with respect to another Two objects moving in opposite directions

“In time and distance questions, always keep the units consistent before applying the formula.”

Aptitude Tip
Key points
  • Distance = Speed × Time.
  • Speed = Distance ÷ Time.
  • Time = Distance ÷ Speed.
  • Use same units before calculation.
  • Average speed is based on total distance and total time.
  • Relative speed depends on direction of movement.
speed distance time average speed relative speed

Visual Understanding

These diagrams show the basic relationship between speed, distance, time, and direction of movement.

Speed, Distance and Time Triangle
D S T Cover the required value and apply the formula
\[ D=S\times T,\quad S=\frac{D}{T},\quad T=\frac{D}{S} \]

The triangle helps remember the three basic formulas.

Object Moving from A to B
A B Motion Distance covered Time taken depends on speed
\[ \text{Distance}=\text{Speed}\times\text{Time} \]

If speed increases, time taken to cover the same distance decreases.

Opposite Direction Relative Speed
A B Opposite directions: speeds are added
\[ \text{Relative Speed}=S_1+S_2 \]

When two objects move towards each other, their relative speed is the sum of their speeds.

Same Direction Relative Speed
Faster Slower Same direction: subtract the speeds
\[ \text{Relative Speed}=S_1-S_2 \]

When objects move in the same direction, use the difference of their speeds.

Important Formulas and Rules

Distance
\[ D=S\times T \]

Distance equals speed multiplied by time.

Speed
\[ S=\frac{D}{T} \]

Speed equals distance divided by time.

Time
\[ T=\frac{D}{S} \]

Time equals distance divided by speed.

Average Speed
\[ \text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}} \]

Do not simply average speeds unless time is equal.

km/h to m/s
\[ 1\text{ km/h}=\frac{5}{18}\text{ m/s} \]

Multiply km/h by \(\frac{5}{18}\).

m/s to km/h
\[ 1\text{ m/s}=\frac{18}{5}\text{ km/h} \]

Multiply m/s by \(\frac{18}{5}\).

Opposite Direction
\[ \text{Relative Speed}=S_1+S_2 \]

Used when two objects move towards each other.

Same Direction
\[ \text{Relative Speed}=S_1-S_2 \]

Subtract smaller speed from larger speed.

Equal Distance Average Speed
\[ \text{Average Speed}=\frac{2xy}{x+y} \]

Used when equal distances are covered at speeds \(x\) and \(y\).

Speed Ratio and Time Ratio
\[ S_1:S_2=T_2:T_1 \]

For the same distance, speed and time are inversely proportional.

Distance Ratio
\[ D_1:D_2=S_1T_1:S_2T_2 \]

Used when both speed and time differ.

Time Saved
\[ \text{Time saved}=T_1-T_2 \]

Used when speed increases and time decreases.

Rule: Always convert units before calculation. If speed is in km/h and time is in hours, distance will be in kilometres. If speed is in m/s and time is in seconds, distance will be in metres.

Common Types of Questions

Basic Speed Questions

Find speed, distance, or time using the basic formula.

  • Find speed
  • Find distance
  • Find time
  • Unit conversion
Average Speed

Based on total distance and total time.

  • Equal distance
  • Different distance
  • Return journey
  • Multiple speeds
Relative Speed

Compare two moving objects based on direction.

  • Opposite direction
  • Same direction
  • Meeting point
  • Overtaking
Time Saved or Late

Based on change in speed and change in time.

  • Speed increased
  • Speed decreased
  • Late arrival
  • Early arrival
Exam approach: Write down the given values under \(S\), \(D\), and \(T\). Then choose the correct formula.
Method Bank
Find Distance

Speed \(=60\) km/h, time \(=3\) h.

\[ D=60\times3=180\text{ km} \]
Find Speed

Distance \(=240\) km, time \(=4\) h.

\[ S=\frac{240}{4}=60\text{ km/h} \]
Find Time

Distance \(=150\) km, speed \(=50\) km/h.

\[ T=\frac{150}{50}=3\text{ h} \]
Equal Distance Average

Speeds \(40\) km/h and \(60\) km/h.

\[ \frac{2xy}{x+y}=\frac{2\times40\times60}{40+60}=48\text{ km/h} \]

Tip: Average speed is not always the simple average of speeds. Use total distance divided by total time.

Time and Distance Solving Flow
Identify S,D,T Check Units Apply Formula Final Answer Values → units → formula → answer
This flow helps avoid unit-based mistakes in speed, distance, and time questions.
\[ D=S\times T \]
\[ \text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}} \]

Step-by-Step Solving Method

Step What to Do Example
Step 1 Identify the given speed, distance, and time. Speed = 60 km/h, Time = 2 h
Step 2 Check whether units are consistent. km/h with hours gives km
Step 3 Choose the required formula. \(D=S\times T\)
Step 4 Substitute the values carefully. \(D=60\times2\)
Step 5 Write the answer with correct unit. Distance = 120 km
Important: If time is given in minutes and speed is in km/h, convert minutes into hours before calculation.

Solved Examples

Question Method Answer
A car travels at 60 km/h for 3 hours. Find the distance. Use:
\[ D=S\times T \]
\[ D=60\times3=180\text{ km} \]
180 km
A person covers 240 km in 4 hours. Find the speed. Use:
\[ S=\frac{D}{T} \]
\[ S=\frac{240}{4}=60\text{ km/h} \]
60 km/h
A bus travels 150 km at 50 km/h. Find the time taken. Use:
\[ T=\frac{D}{S} \]
\[ T=\frac{150}{50}=3\text{ hours} \]
3 hours
Convert 72 km/h into m/s. Multiply by \(\frac{5}{18}\).
\[ 72\times\frac{5}{18}=20\text{ m/s} \]
20 m/s
Convert 15 m/s into km/h. Multiply by \(\frac{18}{5}\).
\[ 15\times\frac{18}{5}=54\text{ km/h} \]
54 km/h
A person travels equal distances at 40 km/h and 60 km/h. Find average speed. For equal distances:
\[ \text{Average Speed}=\frac{2xy}{x+y} \]
\[ \frac{2\times40\times60}{40+60}=48\text{ km/h} \]
48 km/h
Two persons move in opposite directions at 5 km/h and 7 km/h. Find relative speed. Opposite direction means add speeds.
\[ 5+7=12\text{ km/h} \]
12 km/h
Two persons move in the same direction at 12 km/h and 8 km/h. Find relative speed. Same direction means subtract speeds.
\[ 12-8=4\text{ km/h} \]
4 km/h

Note: In average speed questions, use total distance divided by total time. Do not blindly average the speeds.

Common Traps and Shortcuts

Common Traps
  • Using km/h with minutes without converting time to hours.
  • Using m/s with kilometres without converting units.
  • Taking average speed as simple average in all cases.
  • Adding speeds in same-direction relative speed problems.
  • Subtracting speeds in opposite-direction relative speed problems.
  • Forgetting to write the correct unit in final answer.
Useful Shortcuts
  • Distance = Speed × Time.
  • For equal distances, average speed \(=\frac{2xy}{x+y}\).
  • Opposite direction: add speeds.
  • Same direction: subtract speeds.
  • km/h to m/s: multiply by \(\frac{5}{18}\).
  • m/s to km/h: multiply by \(\frac{18}{5}\).
Exam approach: Most mistakes in this topic are unit mistakes. Convert units first, then apply formula.

Practice

A) Multiple Choice Questions
  1. A car travels at 50 km/h for 4 hours. Find the distance.
    100 km 150 km 200 km 250 km
  2. A person covers 180 km in 3 hours. Find speed.
    40 km/h 50 km/h 60 km/h 70 km/h
  3. Convert 36 km/h into m/s.
    5 m/s 10 m/s 15 m/s 20 m/s
  4. Two people move in opposite directions at 8 km/h and 6 km/h. Relative speed is:
    2 km/h 8 km/h 12 km/h 14 km/h
  5. For equal distances at speeds 30 km/h and 60 km/h, average speed is:
    40 km/h 45 km/h 50 km/h 60 km/h
B) Solve the Higher-Order Problems
  1. A bike travels at 45 km/h for 2 hours 30 minutes. Find the distance. (Hint: Convert 2 hours 30 minutes into 2.5 hours.)
  2. A person covers 300 km at 60 km/h. Find the time taken. (Hint: \(T=\frac{D}{S}\).)
  3. A man travels 120 km at 40 km/h and returns at 60 km/h. Find average speed. (Hint: Equal distance average speed formula.)
  4. Two cars move in the same direction at 90 km/h and 70 km/h. Find relative speed. (Hint: Same direction means subtract.)
  5. Convert 25 m/s into km/h. (Hint: Multiply by \(\frac{18}{5}\).)
C) Match the Concept with the Correct Meaning
Concept Correct Meaning
Speed Distance covered per unit time
Distance Total path covered
Time Duration taken to cover distance
Average Speed Total distance divided by total time
Opposite Direction Relative speed is sum of speeds
Same Direction Relative speed is difference of speeds
Aptitude Reminder

Time and Distance questions are based on three values: speed, distance, and time. Keep units consistent, use the correct formula, and be careful with average speed and relative speed.

Task: Create five questions using speed, distance, time, average speed, and relative speed.

Show Suggested Answers
Multiple Choice
  1. 200 km
    \[ D=S\times T=50\times4=200\text{ km} \]
  2. 60 km/h
    \[ S=\frac{D}{T}=\frac{180}{3}=60\text{ km/h} \]
  3. 10 m/s
    \[ 36\times\frac{5}{18}=10\text{ m/s} \]
  4. 14 km/h
    Opposite direction means add speeds.
    \[ 8+6=14\text{ km/h} \]
  5. 40 km/h
    Equal distances:
    \[ \text{Average Speed}=\frac{2xy}{x+y} \]
    \[ \frac{2\times30\times60}{30+60}=40\text{ km/h} \]
Higher-Order Problems
  1. Time \(=2\) hours \(30\) minutes \(=2.5\) hours.
    \[ D=45\times2.5=112.5\text{ km} \]
    Answer = 112.5 km.
  2. Distance \(=300\) km, speed \(=60\) km/h.
    \[ T=\frac{300}{60}=5\text{ hours} \]
    Answer = 5 hours.
  3. Equal distances at 40 km/h and 60 km/h:
    \[ \text{Average Speed}=\frac{2\times40\times60}{40+60} \]
    \[ =\frac{4800}{100}=48\text{ km/h} \]
    Answer = 48 km/h.
  4. Same direction means subtract speeds.
    \[ 90-70=20\text{ km/h} \]
    Answer = 20 km/h.
  5. Convert m/s to km/h:
    \[ 25\times\frac{18}{5}=90\text{ km/h} \]
    Answer = 90 km/h.
Concept Matching
  1. Speed → Distance covered per unit time
  2. Distance → Total path covered
  3. Time → Duration taken to cover distance
  4. Average Speed → Total distance divided by total time
  5. Opposite Direction → Relative speed is sum of speeds
  6. Same Direction → Relative speed is difference of speeds
Clue Explanation

Speed, distance, and time are directly connected. Most problems are solved using one of the three basic formulas, but average speed and relative speed require extra attention.

Exam tips
  • Always check whether time is in hours, minutes, or seconds.
  • Use \(D=S\times T\) for distance.
  • Use \(S=\frac{D}{T}\) for speed.
  • Use \(T=\frac{D}{S}\) for time.
  • For opposite direction, add speeds.
  • For same direction, subtract speeds.
Practice MCQs