guerrero wrote:Hi All ,

Pipes A and B can fill a cistern in 20 and 30 minutes and C can empty it in 15 minutes. If the three are opened and closed one after the other successively for 1 min. each in that order, how soon will the cistern be filled ?

1)180 min
2)160 min
3)167 min
4)187 min


I could calculate part filled in 3 mins = 1/60th Part .

part filled in 177 min = 59/60th

remaining part = 1- 59/60 = i/60

i am stuck after this step . Please help me understand the approach .

thanks in advance !

Let the cistern = 60 units.

A's rate = 60/20 = 3 units per minute.
B's rate = 60/30 = 2 units per minute.
C's rate = 60/15 = -4 units per minute.
When the pipes work in succession, their combined rate for each three-minute cycle = A+B-C = 3+2-4 = 1 unit per cycle.

From here, we can plug in the answers, which represent the time needed to fill the cistern.

Answer choice B: 160 minutes
160/3 = 53 R1.
Here, there will be 53 three-minute cycles (during which all 3 pipes operate in succession) plus 1 extra minute (during which only pipe A operates).
Total number of units filled = 53 + 3 = 56.
Since 60 units are needed to fill the cistern, eliminate B.

Answer choice C: 167
167/3 = 55 R2.
Here, there will be 55 three-minute cycles (during which all 3 pipes operate in succession) plus 2 extra minutes (during which only pipes A and B operate in succession).
Total number of units filled = 55 + 3 + 2 = 60.
Success!

The correct answer is C.

thank you so much , Mitch . Nice approach . Now i get the confidence back