Question

A car travelling with $\frac{2}{5}$ of its actual speed covers 400 km in 16 hours 40 minutes. Find the actual speed of the car.

• A. 60 kmph
• B. 64 kmph
• C. 72 kmph
• D. 68 kmph

Hint:

Always ensure to convert time into a consistent unit (in hours, if working with speed in km/h), and then use the speed formula to calculate the actual speed.

Answer 1

The Correct Option is A

Step 1: Convert time to hours. 
16 hours 40 minutes = 16 + \( \frac{40}{60} \) = 16 + \( \frac{2}{3} \) = \( \frac{50}{3} \) \(\text{ hours.}\)

Step 2: Apply the speed formula. 
We know that Speed = \(\frac{\text{Distance}}{\text{Time}}\)
 Let the actual speed of the car be \( x \) km/h. Since the car is travelling at $\frac{2}{5}$ of its actual speed, its travelling speed is \( \frac{2}{5}x \) km/h. 
The time taken to cover 400 km at \( \frac{2}{5} \)x speed is = \( \frac{400}{\frac{2}{5}x} \) = \( \frac{400 \times 5}{2x} \) = \( \frac{2000}{2x} \) = \( \frac{1000}{x} \) \(\text{ hours.}\)
 \(\text{But we know the time taken is }\) \( \frac{50}{3} \) \text{ hours.} Thus, equating the two expressions for time: \[ \frac{1000}{x} = \frac{50}{3} \] 

Step 3: Solve for \( x \). 
Multiplying both sides by \( x \) and \( 3 \): \[ 1000 \times 3 = 50 \times x \] \[ 3000 = 50x \] \[ x = \frac{3000}{50} = 60 \text{ km/h.} \] 

Step 4: Final Answer 
Thus, the actual speed of the car is 60 km/h. Final Answer: The correct answer is (a) 60 km/h.