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Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?
(XAT 2015)
- a)Pipe A was open for 19 hours
- b)Pipe A was open for 19 hours 30 minutes
- c)Pipe B was open for 19 hours 30 minutes
- d)Pipe C was open for 19 hours 50 minutes
- e)The situation is not possible
Correct answer is option 'C'. Can you explain this answer?
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Three pipes are connected to an inverted cone, with its base at the to...
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Three pipes are connected to an inverted cone, with its base at the to...
**Given Information:**
- Pipe A can fill the cone in 8 hours.
- Pipe B can fill the cone in 12 hours.
- Pipe C can empty the cone in 4 hours.
- When all three pipes are opened, the height of the water inside the cone comes down to 50%.
- Two of the three pipes remain open for 20 hours continuously.
**Approach:**
1. Let's assume that the capacity of the inverted cone is 1 unit.
2. Let's calculate the rate at which each pipe fills or empties the cone.
3. Calculate the combined rate at which the two inlet pipes A and B fill the cone when they are open for 20 hours continuously.
4. Calculate the rate at which the outlet pipe C empties the cone when it is open for 20 hours continuously.
5. Calculate the remaining capacity of the cone after 20 hours.
6. From the remaining capacity, calculate the height of the water inside the cone.
7. Determine the time for which each pipe was open based on the calculated height of the water.
**Calculation:**
Let the capacity of the cone be 1 unit.
Rate of pipe A = 1/8 units per hour
Rate of pipe B = 1/12 units per hour
Rate of pipe C = -1/4 units per hour (negative sign indicates emptying)
Combined rate of pipes A and B = 1/8 + 1/12 = 5/24 units per hour
Rate of pipe C when open for 20 hours = -1/4 * 20 = -5/24 units
Remaining capacity after 20 hours = 1 - (5/24 * 20) = 1 - 5/6 = 1/6 units
Height of water inside the cone after 20 hours = remaining capacity = 1/6 units
Let the time for which pipe A was open be x hours.
Rate of pipe A when open for x hours = 1/8 * x = x/8 units
Rate of pipe B when open for (20 - x) hours = 1/12 * (20 - x) = (20 - x)/12 units
Combined rate of pipes A and B = (x/8) + (20 - x)/12 = (3x + 20 - x)/24 = (2x + 20)/24 units
Rate of pipe C when open for (20 - x) hours = -1/4 * (20 - x) = -(20 - x)/4 units
Rate of filling the cone = combined rate - rate of pipe C
(2x + 20)/24 - (20 - x)/4 = 1/6
Simplifying the equation, we get:
(2x + 20)/24 + (x - 20)/4 = 1/6
(2x + 20 + 6(x - 20))/24 = 1/6
(2x + 20 + 6x - 120)/24 = 1/6
8x - 100 = 4
8x = 104
x = 13
Therefore, pipe A was open for 13 hours.
The time for which pipe B was open = 20 - x = 20 - 13 = 7 hours.
Hence, option C, "
- Pipe A can fill the cone in 8 hours.
- Pipe B can fill the cone in 12 hours.
- Pipe C can empty the cone in 4 hours.
- When all three pipes are opened, the height of the water inside the cone comes down to 50%.
- Two of the three pipes remain open for 20 hours continuously.
**Approach:**
1. Let's assume that the capacity of the inverted cone is 1 unit.
2. Let's calculate the rate at which each pipe fills or empties the cone.
3. Calculate the combined rate at which the two inlet pipes A and B fill the cone when they are open for 20 hours continuously.
4. Calculate the rate at which the outlet pipe C empties the cone when it is open for 20 hours continuously.
5. Calculate the remaining capacity of the cone after 20 hours.
6. From the remaining capacity, calculate the height of the water inside the cone.
7. Determine the time for which each pipe was open based on the calculated height of the water.
**Calculation:**
Let the capacity of the cone be 1 unit.
Rate of pipe A = 1/8 units per hour
Rate of pipe B = 1/12 units per hour
Rate of pipe C = -1/4 units per hour (negative sign indicates emptying)
Combined rate of pipes A and B = 1/8 + 1/12 = 5/24 units per hour
Rate of pipe C when open for 20 hours = -1/4 * 20 = -5/24 units
Remaining capacity after 20 hours = 1 - (5/24 * 20) = 1 - 5/6 = 1/6 units
Height of water inside the cone after 20 hours = remaining capacity = 1/6 units
Let the time for which pipe A was open be x hours.
Rate of pipe A when open for x hours = 1/8 * x = x/8 units
Rate of pipe B when open for (20 - x) hours = 1/12 * (20 - x) = (20 - x)/12 units
Combined rate of pipes A and B = (x/8) + (20 - x)/12 = (3x + 20 - x)/24 = (2x + 20)/24 units
Rate of pipe C when open for (20 - x) hours = -1/4 * (20 - x) = -(20 - x)/4 units
Rate of filling the cone = combined rate - rate of pipe C
(2x + 20)/24 - (20 - x)/4 = 1/6
Simplifying the equation, we get:
(2x + 20)/24 + (x - 20)/4 = 1/6
(2x + 20 + 6(x - 20))/24 = 1/6
(2x + 20 + 6x - 120)/24 = 1/6
8x - 100 = 4
8x = 104
x = 13
Therefore, pipe A was open for 13 hours.
The time for which pipe B was open = 20 - x = 20 - 13 = 7 hours.
Hence, option C, "
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Question Description
Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?(XAT 2015)a)Pipe A was open for 19 hoursb)Pipe A was open for 19 hours 30 minutesc)Pipe B was open for 19 hours 30 minutesd)Pipe C was open for 19 hours 50 minutese)The situation is not possibleCorrect answer is option 'C'. Can you explain this answer? for CAT 2026 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?(XAT 2015)a)Pipe A was open for 19 hoursb)Pipe A was open for 19 hours 30 minutesc)Pipe B was open for 19 hours 30 minutesd)Pipe C was open for 19 hours 50 minutese)The situation is not possibleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?(XAT 2015)a)Pipe A was open for 19 hoursb)Pipe A was open for 19 hours 30 minutesc)Pipe B was open for 19 hours 30 minutesd)Pipe C was open for 19 hours 50 minutese)The situation is not possibleCorrect answer is option 'C'. Can you explain this answer?.
Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?(XAT 2015)a)Pipe A was open for 19 hoursb)Pipe A was open for 19 hours 30 minutesc)Pipe B was open for 19 hours 30 minutesd)Pipe C was open for 19 hours 50 minutese)The situation is not possibleCorrect answer is option 'C'. Can you explain this answer? for CAT 2026 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?(XAT 2015)a)Pipe A was open for 19 hoursb)Pipe A was open for 19 hours 30 minutesc)Pipe B was open for 19 hours 30 minutesd)Pipe C was open for 19 hours 50 minutese)The situation is not possibleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes are connected to an inverted cone, with its base at the top. Two inlet pipes, A and B, are connected to the top of the cone and can fill the empty cone in 8 hours and 12 hours, respectively. The outlet pipe C, connected to the bottom, can empty a filled cone in 4 hours. When the cone is completely filled with water, all three pipes are opened. Two of the three pipes remain open for 20 hours continuously and the third pipe remains open for a lesser time. As a result, the height of the water inside the cone comes down to 50%. Which of the following options would be possible?(XAT 2015)a)Pipe A was open for 19 hoursb)Pipe A was open for 19 hours 30 minutesc)Pipe B was open for 19 hours 30 minutesd)Pipe C was open for 19 hours 50 minutese)The situation is not possibleCorrect answer is option 'C'. Can you explain this answer?.
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