IAS 2015 — CSAT Maths

Correct Option (B)

The problem requires calculating the average speed for a journey where the distance traveled in each direction is equal. The correct average speed is calculated as 48 km/hr. However, this value is not present in the provided options (1, 2, 3, 4).

• Given:
• Speed from A to B (V₁) = 40 km/hr.
• Speed from B to A (V₂) = 60 km/hr.
• The formula for average speed when equal distances are covered at different speeds is:

Average Speed = `$= \frac{2V_{1}V_{2}}{V_{1} + V_{2}}$=V1​+V2​2V1​V2​​`

• Substituting the given values:

Average Speed = `$= \frac{2 \times 40 \times 60}{40 + 60}$=40+602×40×60​`

Average Speed = `$= \frac{4800}{100}$=1004800​`

Average Speed = 48 km/hr.

Incorrect Options:

• Option 1 (45 km/hr): This value is not derived from the correct formula for average speed over equal distances. The accurately calculated average speed is 48 km/hr.

• Option 2 (4 km/hr): This value is significantly lower than both individual speeds and the correctly calculated average speed, indicating a conceptual or computational error.

• Option 3 (50 km/hr): This value is obtained by calculating the simple arithmetic mean of the two speeds `$= \frac{40 + 60}{2} = 50$=240+60​=50` km/hr. This method is incorrect for determining average speed when different speeds are maintained over equal distances, as the time spent at each speed is unequal. The car spends more time traveling at the slower speed, thus the average speed must be less than the simple arithmetic mean.

• Option 4 (55 km/hr): This value does not align with the correct application of the average speed formula for equal distances. It is also higher than the calculated correct average speed of 48 km/hr.