Correct Answer - Option 2 : 30/11
Given:
Time to complete the work by A and B together = 15 days
Time to complete the work by B and c together = 20 days
A worked = 8 days
B worked = 10 days
C worked = 3 days
Calculations:
Let the total work be (LCM of 15 and 20) 60 units.
1 day work of A and B together = 60/15
⇒ 4 units
1 day work of B and C together = 60/20
⇒ 3 units
A × 8 + B × 10 + C × 3 = 60 units
⇒ A × 8 + B × (8 + 2) + C × (2 + 1) = 60
⇒ 8A + 8B + 2B + 2C + C = 60
⇒ 8(A + B) + 2(B + C) + C = 60
⇒ 8(4) + 2(3) + C = 60
⇒ 32 + 6 + C = 60
⇒ 38 + C = 60
⇒ C = 22 units/day
Time taken by C to complete whole work = 60/22
⇒ 30/11 days
∴ C can complete the whole work alone in 30/11 days