Correct Answer - Option 1 : 18 days
Given:
A can do the work in 12 days
B can do the work in 24 days
A, B, C can do the work in 72/11 days
Calculation:
A's 1 days work = 1/12
B's 1 days work = 1/24
⇒ (A + B + C)'s 1 days work = 1/12 + 1/24 + 1/C
⇒ 1/12 + 1/24 + 1/C = 11/72
⇒ 1/C = 1/36
C alone can complete the work in 36 days.
∴ Time taken by C to complete half of work = 36 × 1/2 = 18 days
Time taken by a person to complete a/b fraction of work = a/b × (Number of days in which person alone can complete work)