Wage calculation with overtime: A worker is paid ₹ 5 per hour for regular time and ₹ 8 per hour for overtime. A regular working day has 8 hours and a regular week has 5 working days. Over 4 weeks he earned a total of ₹ 920 and he was present on all regular working days. What is the total number of hours (regular + overtime) that he worked in those 4 weeks?

Difficulty: Easy

Correct Answer: 175 h

Explanation:


Introduction / Context:
This is a classic wages-and-time problem that mixes a fixed schedule of regular hours with higher-paid overtime hours. The goal is to separate regular pay from overtime pay and then recover the total number of hours from the given total earnings.


Given Data / Assumptions:

  • Regular wage = ₹ 5 per hour.
  • Overtime wage = ₹ 8 per hour.
  • Regular working day = 8 hours; regular week = 5 days.
  • He worked all regular days for 4 weeks.
  • Total earnings across 4 weeks = ₹ 920.


Concept / Approach:
First compute the guaranteed regular hours and the corresponding regular-pay amount. Subtract this from the total earnings to isolate how much was paid at the overtime rate. Convert overtime earnings to overtime hours, then add regular hours to obtain the total hours worked.


Step-by-Step Solution:

Regular hours per week = 5 days * 8 h = 40 h.Regular hours in 4 weeks = 4 * 40 = 160 h.Regular pay = 160 h * ₹ 5/h = ₹ 800.Overtime earnings = Total − Regular pay = 920 − 800 = ₹ 120.Overtime hours = 120 / 8 = 15 h.Total hours = 160 + 15 = 175 h.


Verification / Alternative check:
Rebuild the wages from hours: 160 h at ₹ 5 is ₹ 800 and 15 h at ₹ 8 is ₹ 120, total ₹ 920. This matches the given earnings, so the hour count is consistent.


Why Other Options Are Wrong:
160 h ignores overtime; 180 h and 200 h imply overtime earnings that would exceed ₹ 120; 168 h does not match the computed overtime component.


Common Pitfalls:
Forgetting that regular hours are fixed by the schedule, or accidentally applying the overtime rate to regular hours. Always separate earnings by rate and then recombine hours at the end.


Final Answer:
175 h

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