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ABHYAS PREP: COMMERCIAL ARITHMETIC · TIME & WORK

Men, days, hours and work (chain rule)

Work done = men × days × hours. Keep the work per man-hour fixed: M₁D₁H₁/W₁ = M₂D₂H₂/W₂.

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Worked examples

Example 1 · level 1

15 workers, working 6 hours a day, finish the building in 20 days. How many days will 6 workers take to finish the building, working 6 hours a day?

  1. 51 days
  2. 8 days
  3. 50 days
  4. 52 days
Show solution
  1. M₁D₁H₁/W₁ = 15 × 20 × 6 / 1 = 1,800 worker-hours per unit.
  2. D₂ = 15 × 20 × 6 × 1 / (6 × 6 × 1).
  3. D₂ = 1,800 / 36 = 50 days.

Answer: 50 days

Example 2 · level 2

21 workers, working 8 hours a day, finish 2 km of wall in 30 days. How many days will 12 workers take to finish 2 km of wall, working 10 hours a day?

  1. 52.5 days
  2. 17.14 days
  3. 42 days
  4. 43 days
Show solution
  1. M₁D₁H₁/W₁ = 21 × 30 × 8 / 2 = 2,520 worker-hours per unit.
  2. D₂ = 21 × 30 × 8 × 2 / (12 × 10 × 2).
  3. D₂ = 10,080 / 240 = 42 days.

Answer: 42 days

Example 3 · level 3

24 workers, working 8 hours a day, finish 2 km of building in 15 days. How many days will 10 workers take to finish 2 km of building, working 6 hours a day?

  1. 6.25 days
  2. 48 days
  3. 49 days
  4. 36 days
Show solution
  1. M₁D₁H₁/W₁ = 24 × 15 × 8 / 2 = 1,440 worker-hours per unit.
  2. D₂ = 24 × 15 × 8 × 2 / (10 × 6 × 2).
  3. D₂ = 5,760 / 120 = 48 days.

Answer: 48 days

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