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:

Given:

Speed 1 (S₁) = 40 km/hr

Speed 2 (S₂) = 45 km/hr

Late time at S₁ = 10 min = (10 ÷ 60) hr = 1/6 hr

Late time at S₂ = 4 min = (4 ÷ 60) hr = 1/15 hr

Formula used:

Time = Distance ÷ Speed

Difference in time = Late time difference

⇒ Distance = Speed × Time

Calculations:

Let the correct time for the train to complete the journey be T hours.

At S₁, total time taken = T + 1/6

At S₂, total time taken = T + 1/15

Distance covered at both speeds is the same:

⇒ Distance = S₁ × (T + 1/6) = S₂ × (T + 1/15)

⇒ 40 × (T + 1/6) = 45 × (T + 1/15)

⇒ 40T + (40 × 1/6) = 45T + (45 × 1/15)

⇒ 40T + 40/6 = 45T + 45/15

⇒ 40T + 20/3 = 45T + 3

⇒ 20/3 - 3 = 45T - 40T

⇒ 20/3 - 9/3 = 5T

⇒ 11/3 = 5T

⇒ T = 11/(3 × 5)

⇒ T = 11/15 hr

Convert T to minutes:

⇒ T = (11/15) × 60

⇒ T = 44 min

∴ The correct answer is option (4).