In a work and time (chain rule) problem, 20 men can build a straight wall 56 meters long in 6 days. Under the same working conditions and efficiency, what length of a similar wall can be built by 35 men in 3 days?

Introduction / Context:
This is a classic work and time question based on the chain rule. It checks your understanding of how the amount of work done (here, length of wall built) varies directly with the number of workers and the number of days, assuming all men work at the same constant rate.

Given Data / Assumptions:
- 20 men can build a wall 56 meters long in 6 days.
- All men work at the same constant rate.
- We want the length of a similar wall built by 35 men in 3 days under the same conditions.
- Work (wall length) is directly proportional to (number of men) * (number of days).

Concept / Approach:
The total work done is proportional to the product of men and days. If r is the length of wall built by one man in one day, then:
- Work = men * days * r.
We first use the initial situation to determine the effective combined rate, and then apply that rate to the new combination of men and days to find the new length of wall.

Step-by-Step Solution:
Step 1: Let r be the length (in meters) built by one man in one day.Step 2: From the first condition: 20 men * 6 days * r = 56 meters.Step 3: So, 120r = 56, giving r = 56 / 120 meters per man-day.Step 4: For 35 men working 3 days, total man-days = 35 * 3 = 105.Step 5: Length built L = 105 * r = 105 * (56 / 120).Step 6: Simplify: 105 / 120 = 7 / 8, so L = 56 * (7 / 8) = 49 meters.

Verification / Alternative check:
We can use direct proportion: length is proportional to men and days. Multiply by factor (35 / 20) for men and (3 / 6) for days: 56 * (35 / 20) * (3 / 6) = 56 * (7 / 4) * (1 / 2) = 56 * (7 / 8) = 49 meters, confirming the same result.

Why Other Options Are Wrong:
46, 47 and 48 meters are all less than the correct proportional result and arise from incorrect partial scaling or arithmetic errors. 50 meters is slightly more than the true value and would require a higher work rate than given. None of these satisfy the proportional relationship exactly.

Common Pitfalls:
Students often forget that both men and days affect the result, or they scale only by men and ignore the change in days, or vice versa. Another mistake is to invert the ratios when applying the chain rule. Always remember that work ∝ men * days, and keep fractions in the correct orientation while simplifying.

Final Answer:
The required length of the similar wall is 49 meters.