3 PIPES

[him1985]

A cistern has 3 pipes A, B and C. A and B call fill it in 3 and hours respectively, and
C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m.
respectively on the same day, the cistern will be empty at
(A) 7 : 12 p.m.
(B) 7 : 15 p.m.
(C) 7 : 10 p.m.
(D) 7 : 18 p.m.

OA : (A)

PLEASE TELL THE TRICK TO SOLVE THIS

[GMATGuruNY]

A cistern has 3 pipes A, B and C. A and B call fill it in 3 and 4 hours respectively, and
C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m.
respectively on the same day, the cistern will be empty at
(A) 7 : 12 p.m.
(B) 7 : 15 p.m.
(C) 7 : 10 p.m.
(D) 7 : 18 p.m.

Let the cistern = 12 units.
Rate for A to fill the cistern = w/t = 12/3 = 4 units per hour.
Rate for B to fill the cistern = w/t = 12/4 = 3 units per hour.
Rate for C to empty the cistern = w/t = 12/1 = 12 units per hour.

From 3-4pm, the amount that A pumps in = 4 units.
From 4-5pm, the amount that A and B pump in together = 4+3 = 7 units.
Total number of units in the cistern = 4+7 = 11 units.
When A, B and C all work together, for every 7 units that A and B pump IN, C pumps OUT 12 units, for a net loss of 5 units per hour.
Time for the 11 units to empty = w/r = 11/5 hours.
5pm + 11/5 hours = 7:12pm.

The correct answer is A.

[kashishh]

A cistern has 3 pipes A, B and C. A and B call fill it in 3 and 4 hours respectively, and
C can empty it in 1 hour. If the pipes are opened at 3 p.m., 4 p.m. and 5 p.m.
respectively on the same day, the cistern will be empty at
(A) 7 : 12 p.m.
(B) 7 : 15 p.m.
(C) 7 : 10 p.m.
(D) 7 : 18 p.m.

I have a doubt on this, dont know if it is relevant !
at 5 pm, when C is working to drain , at that time isn't A+B also filling in the cistern.?

Let the cistern = 12 units.
Rate for A to fill the cistern = w/t = 12/3 = 4 units per hour.
Rate for B to fill the cistern = w/t = 12/4 = 3 units per hour.
Rate for C to empty the cistern = w/t = 12/1 = 12 units per hour.

From 3-4pm, the amount that A pumps in = 4 units.
From 4-5pm, the amount that A and B pump in together = 4+3 = 7 units.
Total number of units in the cistern = 4+7 = 11 units.
When A, B and C all work together, for every 7 units that A and B pump IN, C pumps OUT 12 units, for a net loss of 5 units per hour.
Time for the 11 units to empty = w/r = 11/5 hours.
5pm + 11/5 hours = 7:12pm.

The correct answer is A.

[GMATGuruNY]

I have a doubt on this, dont know if it is relevant !
at 5 pm, when C is working to drain , at that time isn't A+B also filling in the cistern.?

Let the cistern = 12 units.
Rate for A to fill the cistern = w/t = 12/3 = 4 units per hour.
Rate for B to fill the cistern = w/t = 12/4 = 3 units per hour.
Rate for C to empty the cistern = w/t = 12/1 = 12 units per hour.

From 3-4pm, the amount that A pumps in = 4 units.
From 4-5pm, the amount that A and B pump in together = 4+3 = 7 units.
Total number of units in the cistern = 4+7 = 11 units.
When A, B and C all work together, for every 7 units that A and B pump IN, C pumps OUT 12 units, for a net loss of 5 units per hour.
Time for the 11 units to empty = w/r = 11/5 hours.
5pm + 11/5 hours = 7:12pm.

The correct answer is A.

Yes. Note the portion in red above. When the 3 pumps work together:
A and B pump IN 7 units every hour.
C pumps OUT 12 units every hour.
The NET LOSS = 7-12 = 5 units per hour.