Inferring efficiency ratio from a scaled comparison The work done by 8 men and 4 boys in 1 day is 7 times the work done by 1 man and 1 boy in 1 day. What is the ratio of the daily work of 1 man to that of 1 boy?

Introduction / Context:
Scaled comparisons let us deduce relative efficiencies. Here, a large crew’s one-day output equals seven times a small crew’s one-day output, which yields a linear equation in the man and boy daily rates.

Given Data / Assumptions:

• (8 men + 4 boys) in 1 day = 7 × (1 man + 1 boy) in 1 day.
• Let daily rate(man) = M and daily rate(boy) = B.

Concept / Approach:
Translate the sentence into 8M + 4B = 7(M + B). Solve for M in terms of B to get the ratio M:B.

Step-by-Step Solution:

Verification / Alternative check:
Substitute M = 3B: LHS = 8(3B) + 4B = 24B + 4B = 28B; RHS = 7(3B + B) = 7(4B) = 28B. Balanced.

Why Other Options Are Wrong:
2 : 1, 1 : 1, 1 : 2 do not satisfy the equality after substitution.

Common Pitfalls:
Dropping coefficients or misplacing terms when moving 7(M + B) across the equality.

Final Answer:
3 : 1