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If A complete a job in 20 min and B in 30 mins. if they do the same job together how much time will they take?

If A complete a job in 20 min and B in 30 mins. if they do the same job together how much time will they take?

  • (a) 15 minutes
  • (b) 20 minutes
  • (c) 25 minutes
  • (d) 12 minutes
Solution:
  • Step 1: Work rates A takes 20 minutes to finish the job, so A works at a rate of 1/20 of the job per minute. B takes 30 minutes to finish the job, so B works at a rate of 1/30 of the job per minute.
  • Step 2: Put the rates together The combined rate will be the sum of the two work rates: A + B = 1/20 + 1/30. To add the fractions, use a denominator of 60: 1/20 has a denominator of 60, so it becomes 3/60. Similarly, the denominator of the second fraction, 1/30, will become 2/60. Therefore, - The combined rate will be the sum of the two fractions: 3/60 + 2/60 = 5/60 = 1/12 of the job per minute.
  • Step 3: Time to finish together If they work together, the job will be completed in 12 minutes.
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