The question consists of four statements numbered "I, II, III and IV" given below it. You have to decide whether the data provided in any of the statements alone is sufficient to answer the question. Time taken by 'A', 'B' and 'C' to complete a work together is 12 days, which is (2/3) of the time taken by 'A' to complete the work alone. Find the time taken by 'B' to complete the work alone. Statement I: Time taken by 'B' and 'C' to complete twice the work together is 72 days. Statement II: 'B' starts the work alone. After 10 days, 'B' left the work and 'A' worked alone for 9 days, and the remaining work was completed by 'C' alone in 30 days. Statement III: 'A' and 'C' worked alternately for a day (starting with 'A'). After 18 days, both of them left the work, and the remaining work was completed by 'B' in 24 days. Statement IV: Time taken by 'D' to complete the work is 12 days, which is (1/3) less than the time taken by 'A' to complete the work.

Time taken by 'A' to complete the work = (3/2) × 12 = 18 days Let the total work be 36 units (LCM of 18 and 12) Efficiency of 'A' = (36/18) = 2 units/day Combined efficiency of 'A', 'B' and 'C' = (36/12) = 3 units/day Combined efficiency of 'B' and 'C' = 3 - 2 = 1 unit/day Let the efficiency of 'B' be 'n' units/day Efficiency of 'C' = (1 - n) units/day Statement I: 1 × 72 = 2 × 36 72 = 72 We cannot solve further. So, data in statement I alone is not sufficient to answer the question. Statement II: 10n + 9 × 2 + 30 × (1 - n) = 36 Or, 10n + 18 + 30 - 30n = 36 Or, 48 - 20n = 36 Or, 20n = 12 Or, 'n' = 0.6 Required time = 36 ÷ 0.6 = 60 days So, data in statement II alone is sufficient to answer the question. Statement III: Work done in first 2 days = 2 + (1 - n) = (3 - n) units Work done in first 18 days = 9 × (3 - n) = (27 - 9n) units 27 - 9n + 24n = 36 Or, 15n = 9 Or, 'n' = 0.6 Required time = 36 ÷ 0.6 = 60 days So, data in statement III alone is sufficient to answer the question. Statement IV: Time taken by 'D' to complete the work = 12 days We cannot solve further. So, data in statement IV alone is not sufficient to answer the question. Therefore, only statements II and III alone are sufficient to answer the question. Hence, option c.