Absence-fine wage puzzle: A worker is hired for a 50-day job with the rule: he earns ₹ 12 for each day worked but is fined ₹ 6 for each day absent. After the job ends, he receives ₹ 420 in net payment. For how many days did he not work?

Introduction / Context:
This wage question mixes earnings for working days with a penalty for absences. The essential idea is to set up a simple linear expression for the net amount received and then solve for the number of absent days.

Given Data / Assumptions:

• Total scheduled days = 50
• Pay per working day = ₹ 12
• Fine per absent day = ₹ 6
• Net payment received = ₹ 420

Concept / Approach:
If the worker is absent for x days, he works for (50 − x) days. Net pay equals earnings for worked days minus fines for absent days. Set that equal to ₹ 420 and solve for x.

Step-by-Step Solution:
Let x = number of absent daysNet = 12*(50 − x) − 6*x= 600 − 12x − 6x = 600 − 18xGiven net = 420 ⇒ 600 − 18x = 42018x = 180 ⇒ x = 10

Verification / Alternative check:
Work days = 40 ⇒ earnings = 40 * 12 = ₹ 480; absent days = 10 ⇒ fine = 10 * 6 = ₹ 60; net = 480 − 60 = ₹ 420, which matches the data.

Why Other Options Are Wrong:
15 or 20 days absent would over-deduct, producing net far below ₹ 420.5 days absent would yield ₹ 540 net, which is too high.

Common Pitfalls:
Adding the fine instead of subtracting; forgetting that working and absent days must sum to 50; arithmetic slips when distributing 12 over (50 − x).

Final Answer:
10 days