Question : 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?
Option 1: 8 days
Option 2: 6 days
Option 3: 7 days
Option 4: 9 days
Correct Answer: 9 days
Solution :
Let the total work = Least Common Multiple of 18, 27, 54 = 54 units
Efficiency of S
1
+ S
2
= $\frac{54}{18}$ = 3
Efficiency of S
2
+ S
3
= $\frac{54}{27}$ = 2
Efficiency of S
3
+ S
1
= $\frac{54}{54}$ = 1
Combine efficiency of 2(S
1
+ S
2
+ S
3
) = 6 units/day
⇒Efficiency of (S
1
+ S
2
+ S
3
) = 3 units/day
⇒ Half work = $\frac{54}{2}$ = 27
⇒ Time is taken to finish 50% of work by all the three together = $\frac{27}{3}$ = 9
Hence, the correct answer is 9 days.
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