Multiple choice

A, B, and C together can finish a place of work in 12 days. A and C together work twice as much as B, A and B together work thrice as much as C. In what time ( day ) could each do it separately

  1. 144/5, 36, 48

  2. 36, 48, 144/5

  3. 48, 144/5, 36

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let work rates be A, B, C. A+B+C = 1/12. A+C = 2B implies 3B = 1/12, so B = 1/36. A+B = 3C implies 4C = 1/12, so C = 1/48. Then A = 1/12 - 1/36 - 1/48 = (12-4-3)/144 = 5/144. Time taken: A=144/5, B=36, C=48.

AI explanation

Let the daily work units of A, B, and C be a, b, and c. Given a plus c equals 2b and a plus b equals 3c, we substitute these into the combined rate equation a plus b plus c equals 1/12. Replacing a plus c with 2b gives 3b equals 1/12, so b equals 1/36, meaning B takes 36 days. Replacing a plus b with 3c gives 4c equals 1/12, so c equals 1/48, meaning C takes 48 days. Substituting b and c back into a plus b equals 3c gives a equals 5/144, meaning A takes 144/5 days. The times for A, B, and C are 144/5 days, 36 days, and 48 days respectively.

Keep practicing — related questions