Multiple choice

A and B can do a piece of work in 12 days B and C in 15 days C and A in 20 days then that numbers of days taken by A B and C together to finish the work are

  1. 10 days

  2. 12 days

  3. 14 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

2(A+B+C) = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5. A+B+C = 1/10. Days = 10.

AI explanation

Let the total work be the least common multiple of 12, 15, and 20, which is 60 units. The combined rates are 5 units per day for A and B, 4 units per day for B and C, and 3 units per day for C and A. Adding these three equations gives 2 times the combined rate of A, B, and C as 12 units per day, so their actual combined rate is 6 units per day. Dividing the 60 units of work by 6 units per day gives 10 days. Together they take 10 days.

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