Question

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:

• A. 34 min
• B. 45 min
• C. 44 min
• D. 24 min

Answer 1

Answer:

C. 44 min

Let correct time = (t) hours and distance = (d)

Case 1:

Speed = 40 km/hr, late by 10 min = $(t + \frac{10}{60})$

$d = 40\left(t + \frac{1}{6}\right)$

Case 2:

Speed = 45 km/hr, late by 4 min = $(t + \frac{4}{60} = t + \frac{1}{15})$

$d = 45\left(t + \frac{1}{15}\right)$

Equate both:

$40\left(t + \frac{1}{6}\right) = 45\left(t + \frac{1}{15}\right)$

Expand:
$40t + \frac{40}{6} = 45t + \frac{45}{15}$

$40t + \frac{20}{3} = 45t + 3$

Solve:

$\frac{20}{3} - 3 = 45t - 40t$

$\frac{20}{3} - \frac{9}{3} = 5t$

$\frac{11}{3} = 5t$

$t = \frac{11}{15} \text{ hours}$

Convert to minutes:

$\frac{11}{15} \times 60 = 44 \text{ minutes}$

Final Answer: 44 minutes