An industrial loom weaves cloth at a constant rate of 1.14 metres of cloth every second. Approximately how many seconds will it take this loom to weave a total of 52 metres of cloth?

Introduction:
This problem is a straightforward application of the formula time = distance / speed, where distance is the length of cloth to be woven and speed is the weaving rate of the loom. Such questions are very common in quantitative aptitude under the topic of speed, time, and distance, or rate and work problems.

Given Data / Assumptions:
Weaving speed of the loom = 1.14 metres per second. Required length of cloth = 52 metres. The loom is assumed to operate at a constant speed without interruption. We need an approximate time in seconds.

Concept / Approach:
The relation between distance, speed, and time is: time = distance / speed. Here, distance is the total cloth length, speed is metres per second, and time will naturally come out in seconds. We just substitute the given values and compute the division carefully, then round the result to two decimal places to match the options.

Step-by-Step Solution:
Step 1: Write the formula. time = distance / speed. Step 2: Substitute the given values. time = 52 / 1.14 seconds. Step 3: Perform the division. 52 / 1.14 ≈ 45.6140 seconds. Step 4: Round to two decimal places. Rounded value ≈ 45.61 seconds. Therefore, the loom takes approximately 45.61 seconds to weave 52 metres of cloth.

Verification / Alternative check:
We can check quickly by multiplying the result back by the speed: 1.14 * 45.61 ≈ 52.0 metres (approximately). This confirms that our computed time is consistent with the original distance when multiplied by the weaving rate.

Why Other Options Are Wrong:
29.32 sec and 39.25 sec correspond to weaving speeds that are too high, implying more cloth would be woven than 52 metres in those times. 42.51 sec is closer but still underestimates the time, which would produce less than 52 metres. 52.14 sec would overshoot the distance, producing more than 52 metres at the given speed.

Common Pitfalls:
Learners sometimes invert the formula and accidentally compute speed / distance, or they round intermediate values too aggressively. It is better to keep sufficient decimal precision until the final step, then round only once to match the required accuracy. Another common error is misreading the units and mixing up seconds and minutes, which does not happen here if you carefully track the units as metres per second and seconds.

Final Answer:
The loom will take approximately 45.61 seconds to weave 52 metres of cloth.