If a train runs at 40 km/hr, it reaches its destination late by 10 min, but if it runs by 45 km/hr, it is late by 4 min. The correct time for the train to complete the journey is:

Correct option is C

Given:

- Speed 1 = 40 km/hr => Delay = 10 minutes

- Speed 2 = 45 km/hr => Delay = 4 minutes

- Difference in time = 6 minutes = 6/60 = 1/10 hour

Formula Used:

- Time =  $$\frac{Distance }{Speed}$$​​

- Difference in time = $$\text{Distance} \times \left(\frac{1}{\text{Speed}_1} - \frac{1}{\text{Speed}_2}\right)$$​​

Solution:

Let the actual time taken be T hours, and let the distance be D km.

Using the difference in time formula:

​$$\frac{1}{10} = D \times \left(\frac{1}{40} - \frac{1}{45}\right) \\\ \\= D \times \left(\frac{45 - 40}{40 \times 45}\right) = D \times \frac{5}{1800} = \frac{D}{360} \\\ \\\Rightarrow \frac{1}{10} = \frac{D}{360} \Rightarrow D = 36\ \text{km}$$​​

Now use D = 36 km in any speed formula to get actual time:

At correct time, the train must take (40 km/hr time − 10 minutes):

Time = $$\frac{\text{Distance}}{\text{Speed}} = \frac{36}{40} = 0.9\ \text{hr} = 54\ \text{minutes}$$​  

Correct time = 54 minutes − 10 minutes = 44 minutes

44 minutes 

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