Question

With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 30 km/hr, it is late by 36 minutes. The total distance travelled by train is

• A. 72 km
• B. 78 km
• C. 60 km
• D. 40 km

Answer 1

The Correct Option is A

To solve this problem, let's find out the total distance travelled by the train using the given speed and time conditions.

Let the time taken by the train to reach its destination on time be \(t\) hours at an average speed of 40 km/hr.

1. The formula to calculate distance is given by: \(\text{Distance} = \text{Speed} \times \text{Time}\). Hence, with a speed of 40 km/hr, the distance covered in time \(t\) is: \(\text{Distance} = 40 \times t\).
2. When the speed is reduced to 30 km/hr, the train is late by 36 minutes. Converting 36 minutes to hours, we get: \(36 \text{ minutes} = \frac{36}{60} \text{ hours} = \frac{3}{5} \text{ hours}\).

Therefore, at 30 km/hr, the time taken to cover the same distance becomes \(t + \frac{3}{5}\)hours.

1. Using the formula again for the reduced speed: \(\text{Distance} = 30 \times (t + \frac{3}{5})\).
2. We now have two expressions for the distance:
   • 40 km/hr speed: \(40t\)
   • 30 km/hr speed: \(30(t + \frac{3}{5})\) 

Since both expressions represent the same total distance, equate them to solve for \(t\):

\(40t = 30(t + \frac{3}{5})\)

1. Expand and simplify: \(40t = 30t + 18\)
2. Rearrange to find \(t\): \(40t - 30t = 18\)
3. Thus, \(10t = 18\)
4. Solve for \(t\): \(t = \frac{18}{10} = 1.8 \text{ hours}\)

Finally, calculate the distance using the value of \(t\) at the speed of 40 km/hr:

\(\text{Distance} = 40 \times 1.8 = 72 \text{ km}\)

Therefore, the total distance travelled by the train is 72 km.

The correct answer is: 72 km