Mathematics · Time and Work

A can finish a work alone in [x + 20] days, and B can finish it alone in [x + 10] days. A is 25% less efficient than B. A works for 10 consecutive days and then takes a 1-day break, repeating this cycle until the work is done in [n + 3] days. Similarly, B works 6 days continuously and takes a 2-day break, completing the task in [m + 2] days. D completes the same task in (m - 12) days, and C completes it in [n + 20] days. Which of the following statements is true? I) B and C together complete the work in [x + 4] days. II) A and D together complete the work in [(n/2) - 3] days. III) The sum of m and n is a perfect cube.