Multiple choice

A and B can complete a task in 70 days, B and C can complete it in 52.5 days while C and A can do the same task together in 42 days. How many days will each of A, B, and C take to complete the task individually?

  1. 105, 210 and 70

  2. 56, 84 and 168

  3. 70, 10 and 105

  4. 84, 168 and 56
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C's individual days be a, b, c. Combined rates: A+B = 1/70, B+C = 1/52.5 = 2/105, C+A = 1/42. Adding all three: 2(A+B+C) = 1/70 + 2/105 + 1/42. LCD of 70, 105, 42 is 210. So: 2(A+B+C) = 3/210 + 4/210 + 5/210 = 12/210 = 2/35. Thus A+B+C = 1/35. To find individual rates: (A+B+C) - (B+C) = A = 1/35 - 2/105 = 3/105 - 2/105 = 1/105, so A = 105 days. Similarly, B = 1/35 - 1/42 = 6/210 - 5/210 = 1/210, so B = 210 days. And C = 1/35 - 1/70 = 2/70 - 1/70 = 1/70, so C = 70 days. The answer (105, 210, 70) matches option A. However, the topic is incorrectly listed as 'Clocks & Calendars/Leap Year' when it should be 'Time and Work'.

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