A passenger train departs from Delhi at 6 p m for Mumbai At 9 p m an express train whose average spe...........

Quantitative Aptitude (CDS) Time & distance

A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m., an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km?

4 p.m

2 a.m.

12 midnight

6 a.m.

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Explanation:

Let time taken passenger train = t Time taken by express train = t + 3 When distance = 540 Km Then according to question,
540/t - 540/t+30 = 15
$\small =>540 (\frac{t+3-t}{t(t+3)})$
$\small =>540 \times 3 = 15(t^{2}+3t)$
Solving we get t= 9 or t = -12(not possible)
So t = 9 hours
Hence expression train will take 9 hr
i.e. 9 Pm + 9 hr = 6 AM