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The ratio between the efficiency of pipe Q and R is 4:3 respectively. Pipe S alone can empty the completely filled tank in 30 hours. If all the pipes P, Q, R and S are opened, then the empty tank can be filled in 48 hours. The time taken by pipe Q alone to fill the entire tank is 1.5 times the time taken by pipe P alone to fill the entire tank. Find out the time taken by pipe P and R together to fill 30% of the tank. It is assumed that except pipe S all the pipes are filling pipes.
- a)6 hours
- b)8 hours
- c)12 hours
- d)9 hours
- e)None of the above
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The ratio between the efficiency of pipe Q and R is 4:3 respectively....
Let’s assume the capacity of the tank is 480 units.
Pipe S alone can empty the completely filled tank in 30 hours.
Efficiency of pipe S = 480/30 = -16 units/hour (Here negative sign represents that the pipe is emptying the tank.)
If all the pipes P, Q, R and S are opened, then the empty tank can be filled in 48 hours.
Efficiencies of pipe P, Q, R and S together = 480/48 = 10
Efficiencies of pipe P, Q and R together = 10 - (-16) = 10 + 16 = 26 units/hour Eq.(i)
The ratio between the efficiency of pipe Q and R is 4 : 3 respectively. Eq.(ii)
The time taken by pipe Q alone to fill the entire tank is 1.5 times the time taken by pipe P alone to fill the entire tank.
So the ratio between the time taken by pipe P and Q alone to fill the tank is 2:3. As we know that time and efficiency are inversely proportional to each other. Hence the ratio between the efficiency of pipe P and Q will be 3:2 respectively. Eq.(iii)
From Eq.(ii) and Eq.(iii), the ratio between the efficiency of pipe P, Q and R is 6:4:3 respectively.
From Eq.(i), the total efficiency of pipe P, Q and R together is 26.
Efficiency of pipe Q = 26 of (4/13) = 8 units/hour
Efficiency of pipe P and R together = 26-8 = 18 units/hour
Time taken by pipe P and R together to fill 30% of the tank = (480/18) of 30%
= 8 hours
Hence, option b is the correct answer.
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Community Answer
The ratio between the efficiency of pipe Q and R is 4:3 respectively....
To find the time taken by pipe P and R together to fill 30% of the tank, we need to determine the individual efficiencies of pipe P and R.
Let's assume that the efficiency of pipe P is x, which means that pipe Q has an efficiency of 1.5x and pipe R has an efficiency of (3/4)x.
We are given that pipe S alone can empty the completely filled tank in 30 hours. This implies that the efficiency of pipe S is 1/30, as it can empty the tank in 30 hours.
We are also given that if all the pipes P, Q, R, and S are opened, the empty tank can be filled in 48 hours. This implies that the combined efficiency of all the pipes is 1/48.
Using this information, we can set up the following equation:
x + 1.5x + (3/4)x - 1/30 = 1/48
Simplifying the equation, we get:
(13/4)x - 1/30 = 1/48
Multiplying through by the common denominator, we get:
(13/4)x - (1/30)(120/120) = (1/48)(120/120)
(13/4)x - 4/120 = 5/120
(13/4)x - 1/30 = 1/24
To further simplify the equation, we can convert the fractions to a common denominator:
(13/4)x - (1/30)(4/4) = (1/24)(5/5)
(13/4)x - 4/120 = 5/120
(13/4)x - 1/30 = 1/24
Now, we can combine the fractions:
(13/4)x - 1/30 = 5/120
(13/4)x - 1/30 = 1/24
Multiplying through by the common denominator, we get:
(13/4)x - 4/120 = 5/120
(13/4)x - 4/120 = 1/24
Simplifying the equation, we get:
(13/4)x = 9/120
(13/4)x = 1/12
Multiplying through by the reciprocal of (13/4), we get:
x = (1/12)(4/13)
x = 1/39
Therefore, the efficiency of pipe P is 1/39, and the efficiency of pipe R is (3/4)(1/39) = 3/156 = 1/52.
To find the time taken by pipe P and R together to fill 30% of the tank, we can add their individual efficiencies:
1/39 + 1/52 = (4/156) + (3/156) = 7/156
The reciprocal of 7/156 gives us the time taken for pipe P and R together:
1 / (7/156) = 156/7 = 22.29 hours
Therefore, the time taken by pipe P and R together to fill 30% of the tank is approximately 22.29 hours, which can be rounded to 22 hours.
Hence, the correct answer is option B) 8 hours.
Let's assume that the efficiency of pipe P is x, which means that pipe Q has an efficiency of 1.5x and pipe R has an efficiency of (3/4)x.
We are given that pipe S alone can empty the completely filled tank in 30 hours. This implies that the efficiency of pipe S is 1/30, as it can empty the tank in 30 hours.
We are also given that if all the pipes P, Q, R, and S are opened, the empty tank can be filled in 48 hours. This implies that the combined efficiency of all the pipes is 1/48.
Using this information, we can set up the following equation:
x + 1.5x + (3/4)x - 1/30 = 1/48
Simplifying the equation, we get:
(13/4)x - 1/30 = 1/48
Multiplying through by the common denominator, we get:
(13/4)x - (1/30)(120/120) = (1/48)(120/120)
(13/4)x - 4/120 = 5/120
(13/4)x - 1/30 = 1/24
To further simplify the equation, we can convert the fractions to a common denominator:
(13/4)x - (1/30)(4/4) = (1/24)(5/5)
(13/4)x - 4/120 = 5/120
(13/4)x - 1/30 = 1/24
Now, we can combine the fractions:
(13/4)x - 1/30 = 5/120
(13/4)x - 1/30 = 1/24
Multiplying through by the common denominator, we get:
(13/4)x - 4/120 = 5/120
(13/4)x - 4/120 = 1/24
Simplifying the equation, we get:
(13/4)x = 9/120
(13/4)x = 1/12
Multiplying through by the reciprocal of (13/4), we get:
x = (1/12)(4/13)
x = 1/39
Therefore, the efficiency of pipe P is 1/39, and the efficiency of pipe R is (3/4)(1/39) = 3/156 = 1/52.
To find the time taken by pipe P and R together to fill 30% of the tank, we can add their individual efficiencies:
1/39 + 1/52 = (4/156) + (3/156) = 7/156
The reciprocal of 7/156 gives us the time taken for pipe P and R together:
1 / (7/156) = 156/7 = 22.29 hours
Therefore, the time taken by pipe P and R together to fill 30% of the tank is approximately 22.29 hours, which can be rounded to 22 hours.
Hence, the correct answer is option B) 8 hours.
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The ratio between the efficiency of pipe Q and R is 4:3 respectively. Pipe S alone can empty the completely filled tank in 30 hours. If all the pipes P, Q, R and S are opened, then the empty tank can be filled in 48 hours. The time taken by pipe Q alone to fill the entire tank is 1.5 times the time taken by pipe P alone to fill the entire tank. Find out the time taken by pipe P and R together to fill 30% of the tank. It is assumed that except pipe S all the pipes are filling pipes.a)6 hoursb)8 hoursc)12 hoursd)9 hourse)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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