Two pipes A and B can fill a 1 / 4th filled cistern in 15 and 20 minut

1.	Two pipes A and B can fill a 1 / 4th filled cistern in 15 and 20 minutes respectively while pipe C can empty that exact 1 / 4th filled cistern in 10 minutes. Find the time required to fill the cistern if all three pipes are open when the cistern itself is empty.1. 20 minutes2. 16 minutes3. 18 minutes4. 24 minutes5. 12 minutes
Answer» Correct Answer - Option 2 : 16 minutes Given: Pipe A and B can fill (1-1 / 4) = 3 / 4^th of the cistern in 15 and 20 minutes respectively. Pipe C can empty 1 / 4^th of the cistern in 10 minutes. Formula used: Total volume = time × rate of resultant water inlet Calculations: Let us assume the total volume of the cistern = 4 × LCM of (15, 20, 10) = 240 lit. A and B can fill 3 / 4^th i.e. (240 × 3 / 4) = 180 lit. in 15 and 20 minutes respectively. C can empty 1 / 4^th i.e. (240 × 1 / 4) = 60 lit in 10 minutes. Inlet capacity for A = 180 / 15 = 12 lit / min Inlet capacity for B = 180 / 20 = 9 lit / min Outlet capacity for C = 60 / 10 = 6 lit / min If three pipes are open at the same time, rate of resultant inlet = (12 + 9 - 6) = 15 lit / min Time required to fill the completely empty cistern = 240 / 15 = 16 min

Two pipes A and B can fill a 1 / 4th filled cistern in 15 and 20 minutes respectively while pipe C can empty that exact 1 / 4th filled cistern in 10 minutes. Find the time required to fill the cistern if all three pipes are open when the cistern itself is empty.1. 20 minutes2. 16 minutes3. 18 minutes4. 24 minutes5. 12 minutes

Answer» Correct Answer - Option 2 : 16 minutes

Given:

Pipe A and B can fill (1-1 / 4) = 3 / 4^th of the cistern in 15 and 20 minutes respectively.

Pipe C can empty 1 / 4^th of the cistern in 10 minutes.

Formula used:

Total volume = time × rate of resultant water inlet

Calculations:

Let us assume the total volume of the cistern = 4 × LCM of (15, 20, 10) = 240 lit.

A and B can fill 3 / 4^th i.e. (240 × 3 / 4) = 180 lit. in 15 and 20 minutes respectively.

C can empty 1 / 4^th i.e. (240 × 1 / 4) = 60 lit in 10 minutes.

Inlet capacity for A = 180 / 15 = 12 lit / min

Inlet capacity for B = 180 / 20 = 9 lit / min

Outlet capacity for C = 60 / 10 = 6 lit / min

If three pipes are open at the same time, rate of resultant inlet = (12 + 9 - 6) = 15 lit / min

Time required to fill the completely empty cistern = 240 / 15 = 16 min