Solution
Given:• A straight highway connects two cities P and Q, and goes via two checkpoints M and N, in that order
• A bus started from P and moved to M at an average speed of 30 mph
• After crossing M, it increased its speed to 50 mph, towards N
• From N, it further increased its speed to 60 mph till it reached Q
To find:• The average speed of the bus throughout the whole journey
Approach and Working: The given scenario can be depicted using the following table:
Let us assume that the distance between P and M is x, between M and N is y, and between N and Q is z.
Therefore, the average speed of the whole journey = (x + y + z) / (x/30 + y/50 + z/60)
Analysing Statement 1• As per the information given in Statement 1, the ratio of time the bus took to cover the distances PM, MN, and NQ respectively is 2:1:3
o Let us assume the time taken for the individual parts of the journey to be 2t, t, and 3t
• As we know the distances are x, y, and z respectively, we can say:
o \(\frac{x}{30}\) = 2t or, x = 60t
o \(\frac{y}{50}\) = t or, y = 50t
o \(\frac{z}{60}\) = 3t or, z = 180t
• We can represent the present scenario as follows:
• Therefore, the average speed = total distance travelled/ total time taken
o Or, average speed = (x + y + z)/(2t + t + 3t) = (60t + 50t + 180t)/6t = \(\frac{290t}{6t} = \frac{145}{3}\) mph
• Hence, Statement 1 is sufficient to answer
Analysing Statement 2• As per the information given in Statement 2, out of the three distances, NQ is 3 times the distance PM and more than 3 times the distance MN
o Given that distance NQ is more than 3 times the distance MN, we cannot get any exact value of MN
• Hence, Statement 2 is not sufficient to answer
Hence, the correct answer is Option A.
Answer: A
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