Anil, Anshika and Anamika can do a certain piece of work in 64 days, 72 days and 96 days, respectively. All of them started working together but after ___ days, Anil and Anshika left the job and the remaining work is done by Anamika alone in ___ days. The values given in which of the following options will fill the blanks in the same order in which is it given to make the above statement true:
I. 24, 4
II. 11, 53.5
III. 18, 27
IV. 12, 50

Let the total work = 576 units (LCM of 64, 72 and 96) Amount of work done by Anil alone in one day = 576/64 = 9 units Amount of work done by Anshika alone in one day = 576/72 = 8 units Amount of work done by Anamika alone in one day = 576/96 = 6 units Amount of work done by Anil , Anshika and Anamika together in one day = 9 + 8 + 6 = 23 units For option A: Amount of work done by Anil , Anshika and Anamika together in 24 days = 23 × 24 = 552 units Amount of work done by Anamika alone in 4 days = 6 × 4 = 24 units Total work done = 552 + 24 = 576 units So, option A can be the answer. For option B: Amount of work done by Anil , Anshika and Anamika together in 11 days = 23 × 11 = 253 units Amount of work done by Anamika alone in 53.5 days = 6 × 53.5 = 321 units Total work done = 253 + 321 = 574 units ≠ 576 units So, option B can’t be the answer. For option C: Amount of work done by Anil, Anshika and Anamika together in 18 days = 23 × 18 = 414 units Amount of work done by Anamika alone in 27 days = 27 × 6 = 162 units Total work done = 414 + 162 = 576 units So, option C can be the answer. For option D: Amount of work done by Anil, Anshika and Anamika together in 12 days = 23 × 12 = 276 units Amount of work done by Anamika alone in 50 days = 6 × 50 = 300 units Total work done = 276 + 300 = 576 units So, option D can be the answer.