Question

A can complete a task alone in 9 days while B takes 13.5 days to do it by herself. Together with C it takes them 4.5 days to complete the task. If C and D together can complete the task in 18 days, then how many days will D need to complete the task by herself?
1. 60
2. 54
3. 48
4. 45

Answer 1

Correct Answer - Option 2 : 54

Given:

A can complete the task alone = 9 days

B can complete the task alone = 13.5 days

A, B, and C complete the task together = 4.5 days

C and D together can complete the task = 18 days

Concept used:

Total work = LCM

Formula used:

Efficiency = (Total work)/(Total time)

Calculations:

Let Total work be LCM of (9, 13.5, 4.5, 18) = 54 units

Person	Days	Total work	Efficiency
A	9 days	54	6
B	(27/2) days	54	4
A + B + C	9/2 days	54	12
C + D	18 days	54	3

 

⇒ Efficiency of A = 54/9 = 6 units

⇒ Efficiency of B = 54/13.5 = 4 units

⇒ Efficiency of C = 12 – (6 + 4) = 2 units

⇒ Efficiency of D = 3 – 2 = 1 unit

D alone can complete the work in = 54/1 = 54 days

∴ D alone can complete the work in 54 days