Work and Wages

“Work and Wages is a vital concept in competitive exams, dealing with how much payment a worker receives based on the amount of work done in a given period of time.”

1. Basic Concepts and Formulas

  • Wages = Daily Rate of Pay × Number of Days Worked
  • Rate of Work = 1 / Time Taken to Complete the Work (in case of individual work)
  • If A and B work together, the combined work rate is: 1/A’s Rate + 1/B’s Rate
  • Wages = (Total Work / Total Time) × Wage Rate
  • If wages are paid for a certain task completed in a given period, the payment is distributed based on the work done by each worker.

2. Type-Wise Questions

  • Type 1: Finding Total Wages for One Person
    Example: A works for 10 days at a daily wage of ₹200. How much will A earn?
    Solution: Total Wages = ₹200 × 10 = ₹2000
  • Type 2: Finding Daily Wage from Total Wages
    Example: A earns ₹2400 for 12 days of work. What is A’s daily wage?
    Solution: Daily Wage = ₹2400 / 12 = ₹200 per day
  • Type 3: Work Done by Two People Together
    Example: A can finish a job in 10 days and B can finish it in 15 days. How much will they both earn if they complete the job together in 6 days?
    Solution: Combined rate = 1/10 + 1/15 = 1/6. In 6 days, they complete 1 full job. If the total wage is ₹1200, their combined wage for the job will be ₹1200.
  • Type 4: Work Done by One Person and Another Joins Later
    Example: A can finish a task in 10 days and B can finish it in 20 days. A works for 4 days, then B joins. How long will they take to finish the task and how much will B earn for the 2 days of work?
    Solution: A’s work in 4 days = 4/10 = 2/5 of the task. The remaining work = 3/5. A and B together can complete the task in (10 × 20) / (10 + 20) = 6.67 days. If the total wage for the task is ₹1000, B will earn ₹1000 × (2/10) = ₹200 for the work done.
  • Type 5: Work Done by Several People with Different Wages
    Example: A can finish a task in 10 days and B can finish it in 15 days. If A and B are paid ₹500 for completing the job together, how much should each person be paid?
    Solution: A’s rate = 1/10, B’s rate = 1/15. Combined rate = 1/10 + 1/15 = 1/6. So, they complete the task together in 6 days. A’s contribution = (1/10) / (1/6) = 3/5. B’s contribution = (1/15) / (1/6) = 2/5. A’s payment = ₹500 × 3/5 = ₹300, B’s payment = ₹500 × 2/5 = ₹200.
  • Type 6: Finding Payment for Part of the Work
    Example: A completes 3/4 of the task in 8 days, and B completes the remaining work in 4 days. How much should A and B be paid for completing a total wage of ₹1200?
    Solution: Total work completed by A = 3/4, B = 1/4. A’s share = (3/4) × ₹1200 = ₹900, B’s share = (1/4) × ₹1200 = ₹300.
  • Type 7: Equal Work Done, Different Wages
    Example: A, B, and C can complete a task in 10, 15, and 30 days, respectively. If their combined payment is ₹9000, how much should each person be paid?
    Solution: Rates of work: A = 1/10, B = 1/15, C = 1/30. Combined rate = 1/10 + 1/15 + 1/30 = 1/5. Time taken to complete the task together = 5 days. A’s payment = ₹9000 × (1/10) / (1/5) = ₹4500, B’s payment = ₹9000 × (1/15) / (1/5) = ₹3000, C’s payment = ₹9000 × (1/30) / (1/5) = ₹1500.
  • Type 8: Work Done by One Person and Another Joins Later
    Example: A works for 6 days, completing 1/3 of the task. B joins and together they finish the rest of the task in 4 days. How much should A and B be paid if the total payment is ₹1200?
    Solution: Work done by A = 1/3. Remaining work = 2/3. A and B’s combined work rate = 2/3 ÷ 4 = 1/6. A’s share = 1/6 × 4 days = 2/3. B’s share = 1/3. A’s payment = ₹1200 × 2/3 = ₹800, B’s payment = ₹1200 × 1/3 = ₹400.
  • Type 9: Payment Proportional to Work Done
    Example: A and B are working together on a task. A works for 6 days, completing 1/2 of the work, while B works for 3 days. How should the payment of ₹1000 be divided?
    Solution: Work done by A = 1/2, work done by B = 3/10. Total work = 1. A’s share = 1/2 × ₹1000 = ₹500, B’s share = 3/10 × ₹1000 = ₹300.
  • Type 10: Work Done by Two People with Different Payment Rates
    Example: A can complete a task in 8 days, while B can complete it in 12 days. They work together to finish the task in 5 days. If their total payment is ₹1500, how much should each person be paid?
    Solution: Combined rate = 1/8 + 1/12 = 5/24. Total time = 5 days. A’s share of the total payment = ₹1500 × (5/24) × (1/8) = ₹625, B’s share = ₹1500 × (5/24) × (1/12) = ₹375.

3. Tips to Remember

  • When work is done by two or more people, always calculate their combined rate before determining the total time or payment.
  • Work is divided according to the rate of work for each person, and payments should be proportional to the work done.
  • If someone works part of the time, their share of the payment depends on the amount of work completed.
  • Always pay attention to the units of work and time to ensure accurate calculations.
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