Multiple choice

Matthew, Noah and Owen can complete a piece of work in 10, 20 and 30 days, respectively. Matthew worked for 5 days and left the job. Then, Noah took up the work, worked for 5 days on it and left. After this, Owen completed the remaining work. If Matthew got $150 for his work, how much amount will Owen get?

  1. $50
  2. $75
  3. $100
  4. $125
  5. $150
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: M=1/10, N=1/20, O=1/30. M worked 5 days (5/10 = 1/2 work). N worked 5 days (5/20 = 1/4 work). Remaining work = 1 - 1/2 - 1/4 = 1/4. Owen does 1/4 work. Since M got 150 for 1/2 work, 1/4 work is worth 75.

AI explanation

Taking the total work as the least common multiple of 10, 20 and 30 gives 60 units. Matthew does 6 units per day, so in 5 days he completes 30 units and earns \$150, meaning the wage is \$5 per unit. Noah does 3 units per day, so in 5 days he completes 15 units, leaving 15 units (60 minus 30 minus 15) for Owen. At \$5 per unit, Owen earns \$75 for his 15 units of work.

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