Arithmetic Aptitude: Time and Distance Practice Questions with Solution – SET 1

📘 Step-by-Step Solution:

🧠 Use the basic formula:

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

Given distance = 600 meters
Time = 5 minutes = \[ 5 \times 60 = 300 \, \text{seconds} \]

Speed in m/s: \[ = \frac{600}{300} = 2 \, \text{m/s} \]

Convert to km/hr: \[ 2 \times \frac{18}{5} = 7.2 \, \text{km/hr} \]

✅ Final Answer: \(\boxed{7.2 \, \text{km/hr}}\)

📘 Step-by-Step Solution:

Let the actual distance be \( x \) km.

Time taken at 10 km/hr = \[ \frac{x}{10} \]
Time taken at 14 km/hr = \[ \frac{x + 20}{14} \]

Given: time is same in both cases.

So, \[ \frac{x}{10} = \frac{x + 20}{14} \]

Cross-multiply: \[ 14x = 10(x + 20) \]
\[ 14x = 10x + 200 \]
\[ 4x = 200 \Rightarrow x = 50 \]

✅ Final Answer: \(\boxed{50 \, \text{km}}\)

📘 Step-by-Step Solution:

Let the total time be 60 minutes (1 hour).

Speed without stoppages = 54 km/h ⇒ Bus would cover: \[ \frac{54}{60} = 0.9 \, \text{km per minute} \]

Speed with stoppages = 45 km/h ⇒ Bus actually covers: \[ \frac{45}{60} = 0.75 \, \text{km per minute} \]

Let the stoppage time be \( x \) minutes.
Then, running time = \( 60 – x \)

Distance actually covered in \( 60 – x \) minutes at 0.9 km/min: \[ 0.9 \times (60 – x) = 45 \]

Simplify: \[ 54 – 0.9x = 45 \]
\[ 0.9x = 9 \Rightarrow x = 10 \]

✅ Final Answer: \(\boxed{10 \, \text{minutes}}\)

📘 Step-by-Step Solution:

Given time = 1 hr 40 min 48 sec

Convert to hours: \[ 1 + \frac{40}{60} + \frac{48}{3600} = 1 + \frac{2}{3} + \frac{2}{150} = \frac{300 + 200 + 4}{180} = \frac{504}{180} = 2.8 \, \text{hrs} \]

Speed = Distance / Time = \( \frac{42}{2.8} = 15 \, \text{km/hr} \)

This is \(\frac{7}{8}\) of actual speed ⇒ Let actual speed be \( x \)
\[ \frac{7}{8}x = 15 \Rightarrow x = \frac{15 \times 8}{7} = \frac{120}{7} = 17.14 \, \text{km/hr} \]

✅ Answer: \(\boxed{\frac{120}{7} = \frac{17}{6}}\) km/hr