Question

At what time will the train reach city A from city B?

I. The train crosses another train of equal length of 300 metres and running in opposite direction in 22.5 seconds.

II. The train leaves city B at 8.15 a.m. for city A situated at a distance of 837 km.

III. The train crosses a lamp post in 15 seconds.

• A. I only
• B. II only
• C. III only
• D. II and Ill only
• E. All I, II and III are required.

Answer 1

The correct option is D

II and Ill only

III gives, speed = $\frac{300}{15}m/s=20m/s=\left(20\times \frac{18}{5}\right)km/hr=72km/hr.$
II gives, time taken = $\left(\frac{837}{72}\right)hrs=\frac{93}{8}hrs=11hrs37min30secs.$
So, the train will reach city A at 7:52:30 p.m.
I gives, relative speed of train = $\frac{600}{22.5}=26.67$

Since I is insufficient as speed and direction of another train is not given, thus statement II and III together determines the time.