Attendance-based pay and fines: A worker is engaged over 120 days. He earns ₹20 for each working day and incurs a deduction (fine) of ₹3 for each non-working day. His total remuneration after 120 days is ₹560. How many days was he absent?

Introduction / Context:
This is a linear equation problem involving separate contributions for working and non-working days. The worker receives a positive amount per working day and a deduction per absence, resulting in a relatively small net amount over a long period, which implies many absences.

Given Data / Assumptions:

• Total calendar days considered = 120
• Payment per working day = ₹20
• Deduction per non-working day = ₹3
• Total remuneration = ₹560

Concept / Approach:
Let w = number of working days and a = number of absences. Then w + a = 120. Net pay = 20w - 3a. Solve the simultaneous equations for a.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 60/70/40: Substituting these in w + a = 120 and 20w - 3a fails to produce ₹560.

Common Pitfalls:

• Misinterpreting the deduction as reducing the pay per working day instead of subtracting per absence.
• Arithmetic mistakes while simplifying 2400 - 23a = 560.

Final Answer: