Daily-wage contract with absences: A laborer is engaged for a fixed number of days for ₹ 5750, but due to absences he receives only ₹ 5000. Assuming the same daily wage throughout and integer numbers of paid days, what is the maximum possible daily wage?

Introduction / Context:
The laborer had a fixed daily wage for a fixed-length engagement, but earned less due to absences. The daily wage must divide both the full contracted amount and the actually paid amount, since both are integer multiples of a constant daily rate. To maximize the daily wage under these conditions, we use the greatest common divisor (GCD) of the two totals.

Given Data / Assumptions:

• Total contracted pay if fully present = ₹ 5750.
• Actual paid due to absences = ₹ 5000.
• Daily wage is constant; number of paid days are integers.

Concept / Approach:
If daily wage = d, then 5750 = N * d and 5000 = n * d for integers N and n. Therefore d must divide both 5750 and 5000. The maximum possible d is gcd(5750, 5000). Compute the GCD to find the largest feasible daily wage consistent with both totals being multiples of d.

Step-by-Step Solution:

Verification / Alternative check:
Any larger daily wage would fail to divide either 5750 or 5000; any smaller common divisor is possible but not maximal.

Why Other Options Are Wrong:
₹ 500 and ₹ 375 do not divide both totals; ₹ 125 divides both but is not the maximum; ₹ 200 is not a common divisor of 5750.

Common Pitfalls:
Treating the problem as a percentage deduction question rather than a divisibility constraint on a constant daily rate.

Final Answer:
₹ 250