The distance between two cities, A and B, is 900 miles. A bus starts

Step 1: Analyse Question Stem

The distance between the two cities, A and B, is 900 miles.

A bus, lets say F, travelling at f miles per hour starts from A for B at 7 am.

Another bus, lets say S, travelling at s miles per hour starts from B for A at 8:30 am.

Therefore, F has travelled alone at its own speed for an hour and a half.
Distance covered by F in this time = f * (\(\frac{3}{2}\)) miles.

We have to find out the value of f.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: The speed of the second bus is 4/7 of the speed of the first bus.

This means, s = \(\frac{4 }{ 7}\) f; in other words, f = (\(\frac{7 }{ 4}\)) * s

Unless we have the value of s, we cannot find the value of f.

The data in statement 1 is insufficient to find a unique value for f.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: The two buses cross each other at 7:00 pm on the same day.

Since bus S started at 8:30 am, the two buses travelled a total distance of (900 – \(\frac{3}{2}\) f) miles in 10.5 hours and crossed each other at 7 pm.

In case of relative speed questions,

Time taken to meet or cross each other = \(\frac{Distance between the objects }{ Relative speed}\).

Substituting the values of time and distance between the objects in the equation above, we can find out relative speed.
However, since the relative speed is the sum of the speeds in this case, we will not be able to find out the value of the individual speeds.

The data in statement 2 is insufficient to find a unique value for f.
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1: The speed of the second bus is 4/7 of the speed of the first bus.
From statement 2: The two buses cross each other at 7:00 pm on the same day.

From statement 1, f = (\(\frac{7}{4}\)) s.

Therefore, relative speed = f + s = \(\frac{11 }{4}\) s

From statement 2, time taken to cross = 10.5 hours

Distance between the objects = 900 – (\(\frac{3}{2}\)) f = 900 – (\(\frac{3}{2}\)) (\(\frac{7}{4}\))s = 900 – (\(\frac{21}{8}\))s.

The above values can be substituted into the equation,

Time taken to meet or cross each other = \(\frac{Distance between the objects }{ Relative speed}\).

Upon doing so, it can be seen that it’s an equation in one unknown, s. The equation can be solved for s and using the value of s, the value of f can be calculated.

The combination of statements is sufficient to find the value of f.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.

The correct answer option is C.