S1 and S2 can do a piece of work together in 18 days, S2 and S3 can do the same work together in 27 days, while S3 and S1 can do it together in 54 days. In how many days can all 3, working together, do 50% of the work?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 9 days
LCM of 18, 27, and 54 is 54.
Let's assume the total work is 54 units.
S1 and S2 can do a piece of work together in 18 days.
Efficiency of S1 and S2 together = 54/18 = 3 units/day ....Eq.(i)
S2 and S3 can do the same work together in 27 days.
The efficiency of S2 and S3 together = 54/27 = 2 units/day ....Eq.(ii)
while S3 and S1 can do it together in 54 days.
Efficiency of S3 and S₁ together = 54/54 = 1 unit/day ....Eq.(iii)
From Eq.(i), Eq. (ii), and Eq. (iii), the total efficiency of all three = (3 + 2 + 1)/2
= 6/2
= 3 units/day
Number of days taken by all 3, working together to do 50% of the work = 50% of 54/3
= 50% of 18
= 1/2 × 18
= 9 days