A gun is fired at a distance of 6.64 km from Ram. He hears the sound 20 seconds later. What is the speed of sound in air (in metres per second)?

Introduction / Context:
This question tests the basic concept of speed, which links distance and time. The situation models how we estimate the speed of sound in air when we see an event first and hear it later, such as a gun being fired far away. Understanding how to convert units and apply the speed formula is very important in aptitude tests and physics based word problems. Here, the numbers are straightforward, so once the units are handled correctly, the calculation becomes simple.

Given Data / Assumptions:

Distance between the gun and Ram = 6.64 km.
Time delay between seeing the gun fired and hearing the sound = 20 seconds.
Sound travels in a straight line from the gun to Ram and its speed is constant over this short interval.
We want the speed of sound expressed in metres per second (m/s).

Concept / Approach:
Speed is defined as distance divided by time. The key formula is:
speed = distance / time Here the distance is given in kilometres, while time is in seconds. Since the options use metres per second, we first convert kilometres into metres. One kilometre is equal to 1000 metres. After the conversion, we substitute the values into the formula and simplify. Checking the order of magnitude is also useful, because the speed of sound in air is known to be a bit more than 300 m/s at normal conditions.

Step-by-Step Solution:
Step 1: Convert distance from kilometres to metres. 6.64 km = 6.64 * 1000 m = 6640 m. Step 2: Use the formula speed = distance / time. speed = 6640 / 20 m/s. Step 3: Perform the division. 6640 / 20 = 332. Therefore, speed of sound = 332 m/s.

Verification / Alternative check:
The commonly quoted approximate speed of sound in air at room temperature is around 330 m/s. Our computed value 332 m/s is very close to this standard reference value, which confirms that the calculation is reasonable. The distance of a few kilometres and a time lag of some tens of seconds are also consistent with this speed range, so both the numerical calculation and real world intuition agree.

Why Other Options Are Wrong:
Option a (664 m/s) is almost exactly double the correct speed and does not match standard physical values for sound in air. Option b (664 km/s) and option d (332 km/s) use kilometres per second, which would be extremely large and unrealistic, even faster than the speed of light in some cases. These are unit traps meant to catch candidates who ignore the units. Only 332 m/s matches both the calculation and realistic physics.

Common Pitfalls:
Common mistakes include forgetting to convert kilometres to metres, using minutes instead of seconds, or dividing the time by the distance instead of distance by time. Another frequent error is to choose an answer with correct numbers but incorrect units. Always check that the final unit matches the requirement of the problem and the answer choices. Working systematically through the unit conversion and formula avoids these issues.

Final Answer:
Therefore, the speed of sound in air in this scenario is 332 m/s.