Solutions

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Question

A train travelled from Station A to Station B at an average speed of 80 kilometres per hour and then from Station B to Station C at an average speed of 60 kilometres per hour. If the train did not stop at Station B, what was the average speed at which the train travelled from Station A to C?

I. The distance that the train travelled from Station A to Station B was 4 times the distance that train travelled from Station B to Station C.

II. The amount of time it took to the train to travel from Station A to Station B is 3 times the amount of time that it took the train to travel from Station B to Station C.


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Hard

Solution

Option D is the correct answer.


Option Analysis

Average speed = total distance/ total time.

Statement I is sufficient: A—–B——-C

Let bc=x, therefore AC=4x, and AB=3x

Thus average speed = 4x/{(3x/80)+(x/60)}

We can easily calculate the value of avg. speed from the above exp. hence sufficient.

Statement II is sufficient: A———B———-C

Let the distance between AB=x and BC=y

x/80=4(y/60) x=(16/3)y————-1)

Average speed = x+y/{(x/80)+(y/60)}

We can substitute the value of x in terms of y in the above expression to find out the average speed. Hence sufficient