Correct Answer - Option 3 : 15 days

Given:

A alone can do the work in = 12 days

B's efficiency = 20% more than A's efficiency

A, B and C together finish the work in = 4 days

Concept used:

Total work = Efficiency × Number of days to finish the work

Calculations:

Let C's 1 day work be 1/C

A's 1 day work = 1/12

B's 1 day work = (120/100) × (1/12) = 1/10

(A + B + C)'s 1 day work = 1/4

⇒ (1/12) + (1/10) + (1/C) = 1/4

⇒ (11/60) + (1/C) = 15/60

⇒ 1/C = (15 – 11)/60

⇒ 1/C = 4/60

⇒ 1/C = 1/15

∴ C alone can finish the whole work in 15 days