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?
Aptitude
Simplification
Difficulty: Easy
Choose an option
Answer
Correct Answer: 80
Explanation
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:
w + a = 120 ⇒ w = 120 - aNet pay: 20w - 3a = 56020(120 - a) - 3a = 5602400 - 20a - 3a = 5602400 - 23a = 560 ⇒ 23a = 1840 ⇒ a = 1840 / 23 = 80Verification / Alternative check:
w = 120 - 80 = 40Net = 20*40 - 3*80 = 800 - 240 = 560 (matches)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:
80