Multiple choice

A, B, and C are skilled labourers, each capable of completing a certain task individually within distinct time frames of 12, 30, and 60 days, respectively. They embarked on a collaborative project, initially working together. However, B chose to depart the project after contributing his expertise for a period of 6 days before completion of the project, while C chose to depart 8 days before completion of the project, then what is the total precise duration required to complete the task?

  1. 12 days

  2. 10 days

  3. 9 days

  4. 8 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total days be T. A works for T days, B for T-6, C for T-8. (T/12) + (T-6)/30 + (T-8)/60 = 1. Multiply by 60: 5T + 2(T-6) + (T-8) = 60. 5T + 2T - 12 + T - 8 = 60. 8T = 80. T = 10.

AI explanation

Using the Least Common Multiple method, let the total work be 60 units, making the daily work of A, B, and C equal to 5, 2, and 1 units respectively. Since B left 6 days before completion and C left 8 days before completion, A worked alone for the last 6 days to complete 30 units, leaving 30 units to be completed by A and C. A and C worked together for those 30 units at a rate of 6 units per day, taking 5 days, which means the total time is 6 days plus 4 days of all three working together. The result is 10 days.

Keep practicing — related questions