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A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes?
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A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another...
Solution:
Given,
- Set X of 10 pipes can fill 70% of the tank in 7 minutes.
- Set Y of 5 pipes fills 3/8 of the tank in 3 minutes.
- Set Z of 8 pipes can empty 5/10 of the tank in 10 minutes.
Let's assume that the tank has a capacity of 100 units.
- So, Set X can fill 70 units of the tank in 7 minutes, i.e., (70/7) units/minute.
- Set Y can fill (3/8)*100 = 37.5 units of the tank in 3 minutes, i.e., (37.5/3) units/minute.
- Set Z can empty (5/10)*100 = 50 units of the tank in 10 minutes, i.e., (5/10) units/minute.
To find out the time taken to fill the tank if all the 23 pipes are opened at the same time, we need to calculate the net flow rate of water in the tank.
Let's denote the net flow rate by F.
- F = (flow rate of water coming in) - (flow rate of water going out).
- Flow rate of water coming in = (flow rate of Set X) + (flow rate of Set Y).
- Flow rate of water going out = (flow rate of Set Z).
So,
- Flow rate of Set X = (70/7) units/minute = 10 units/minute.
- Flow rate of Set Y = (37.5/3) units/minute = 12.5 units/minute.
- Flow rate of Set Z = (5/10) units/minute = -0.5 units/minute (negative sign indicates water is going out of the tank).
Therefore,
- F = (10 + 12.5) - (-0.5) = 23 units/minute.
To fill the tank completely, we need to add 100 units of water. So, the time taken to fill the tank completely is given by:
- Time taken = (100/23) minutes = 4.34 minutes (approx).
Therefore, the correct answer is option (a) 5 minutes.
Note:
- It is important to convert all the given information into a common unit (units/minute, in this case) to calculate the net flow rate.
- The negative sign in the flow rate of Set Z indicates that water is going out of the tank, i.e., Set Z is emptying the tank.
Given,
- Set X of 10 pipes can fill 70% of the tank in 7 minutes.
- Set Y of 5 pipes fills 3/8 of the tank in 3 minutes.
- Set Z of 8 pipes can empty 5/10 of the tank in 10 minutes.
Let's assume that the tank has a capacity of 100 units.
- So, Set X can fill 70 units of the tank in 7 minutes, i.e., (70/7) units/minute.
- Set Y can fill (3/8)*100 = 37.5 units of the tank in 3 minutes, i.e., (37.5/3) units/minute.
- Set Z can empty (5/10)*100 = 50 units of the tank in 10 minutes, i.e., (5/10) units/minute.
To find out the time taken to fill the tank if all the 23 pipes are opened at the same time, we need to calculate the net flow rate of water in the tank.
Let's denote the net flow rate by F.
- F = (flow rate of water coming in) - (flow rate of water going out).
- Flow rate of water coming in = (flow rate of Set X) + (flow rate of Set Y).
- Flow rate of water going out = (flow rate of Set Z).
So,
- Flow rate of Set X = (70/7) units/minute = 10 units/minute.
- Flow rate of Set Y = (37.5/3) units/minute = 12.5 units/minute.
- Flow rate of Set Z = (5/10) units/minute = -0.5 units/minute (negative sign indicates water is going out of the tank).
Therefore,
- F = (10 + 12.5) - (-0.5) = 23 units/minute.
To fill the tank completely, we need to add 100 units of water. So, the time taken to fill the tank completely is given by:
- Time taken = (100/23) minutes = 4.34 minutes (approx).
Therefore, the correct answer is option (a) 5 minutes.
Note:
- It is important to convert all the given information into a common unit (units/minute, in this case) to calculate the net flow rate.
- The negative sign in the flow rate of Set Z indicates that water is going out of the tank, i.e., Set Z is emptying the tank.
Community Answer
A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another...
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A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes?
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A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes?.
A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes?.
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A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes?, a detailed solution for A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes? has been provided alongside types of A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. The third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes. Example 1: How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time? (a) 5 minutes (b) 5 5/ 7 minutes (c) 6 minutes (d) 6 5 /7 minutes? theory, EduRev gives you an
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