Multiple choice

A is thrice as good a workman as B. C alone takes 48 days to paint a house. When working together, A, B and C take 16 days to paint the house. How many days will it take for B alone to paint the house?

  1. 32

  2. 64

  3. 96

  4. 72
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B's rate be x, then A's rate is 3x. C's rate is 1/48. Together (A+B+C) = 1/16. So 3x + x + 1/48 = 1/16. 4x = 1/16 - 1/48 = 3/48 - 1/48 = 2/48 = 1/24. x = 1/96. B takes 96 days.

AI explanation

Let the total work be the least common multiple of 48 and 16, which is 48 units. The efficiency of C is 48 divided by 48, equaling 1 unit per day. The combined efficiency of A, B, and C is 48 divided by 16, equaling 3 units per day, so A and B together have an efficiency of 2 units per day. Since A is thrice as good a workman as B, their efficiency ratio is 3 to 1, making B's individual efficiency 0.5 units per day. Therefore, B alone will take 48 divided by 0.5 days to finish the work, which is 96 days.

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