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The ratio of the efficiency of pipes P, Q and R are 3 : 2 : 1 respectively and Pipe R can fill the tank in 1 hour 12 minutes. Find the time taken by pipes P, Q and R together to fill the tank?
- a)18 minutes
- b)24 minutes
- c)30 minutes
- d)12 minutes
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The ratio of the efficiency of pipes P, Q and R are 3 : 2 : 1 respect...
Given:
Efficiency ratio of pipes P, Q, and R = 3:2:1
Efficiency of pipe R = 1 tank per 1 hour 12 minutes
To find:
Time taken by pipes P, Q, and R together to fill the tank
Solution:
Step 1: Convert the time taken by pipe R into hours
1 hour 12 minutes = 1 + 12/60 = 1 + 0.2 = 1.2 hours
Step 2: Let's assume the efficiency of pipe P, Q, and R as E(P), E(Q), and E(R) respectively.
Step 3: Since the efficiency ratio of pipes P, Q, and R is 3:2:1, we can write the following equations:
E(P) : E(Q) : E(R) = 3x : 2x : x
Step 4: The sum of the individual efficiencies of the pipes gives the combined efficiency:
E(P) + E(Q) + E(R) = 3x + 2x + x = 6x
Step 5: The time taken by the pipes to fill the tank is inversely proportional to their efficiencies.
Therefore, the time taken by pipes P, Q, and R together to fill the tank is 1/6x.
Step 6: Since the efficiency of pipe R is 1 tank per 1.2 hours, we can write the equation:
x = 1 tank / 1.2 hours = 5/6 tank per hour
Step 7: Substituting the value of x in the equation from step 5, we get:
Time taken by pipes P, Q, and R together = 1 / (6 * 5/6) = 1 / 5 = 0.2 hours
Step 8: Convert the time taken into minutes:
0.2 hours * 60 minutes/hour = 12 minutes
Therefore, the time taken by pipes P, Q, and R together to fill the tank is 12 minutes. Hence, the correct answer is option D) 12 minutes.
Efficiency ratio of pipes P, Q, and R = 3:2:1
Efficiency of pipe R = 1 tank per 1 hour 12 minutes
To find:
Time taken by pipes P, Q, and R together to fill the tank
Solution:
Step 1: Convert the time taken by pipe R into hours
1 hour 12 minutes = 1 + 12/60 = 1 + 0.2 = 1.2 hours
Step 2: Let's assume the efficiency of pipe P, Q, and R as E(P), E(Q), and E(R) respectively.
Step 3: Since the efficiency ratio of pipes P, Q, and R is 3:2:1, we can write the following equations:
E(P) : E(Q) : E(R) = 3x : 2x : x
Step 4: The sum of the individual efficiencies of the pipes gives the combined efficiency:
E(P) + E(Q) + E(R) = 3x + 2x + x = 6x
Step 5: The time taken by the pipes to fill the tank is inversely proportional to their efficiencies.
Therefore, the time taken by pipes P, Q, and R together to fill the tank is 1/6x.
Step 6: Since the efficiency of pipe R is 1 tank per 1.2 hours, we can write the equation:
x = 1 tank / 1.2 hours = 5/6 tank per hour
Step 7: Substituting the value of x in the equation from step 5, we get:
Time taken by pipes P, Q, and R together = 1 / (6 * 5/6) = 1 / 5 = 0.2 hours
Step 8: Convert the time taken into minutes:
0.2 hours * 60 minutes/hour = 12 minutes
Therefore, the time taken by pipes P, Q, and R together to fill the tank is 12 minutes. Hence, the correct answer is option D) 12 minutes.
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Community Answer
The ratio of the efficiency of pipes P, Q and R are 3 : 2 : 1 respect...
Pipe R alone fill the tank = 60 + 12 = 72 minutes
Pipe P alone fill the tank = 72 * 1/3 = 24 minutes
Pipe Q alone fill the tank = 72 * 1/2 = 36 minutes
Pipes P, Q and R together to fill the tank = 1/24 + 1/36 + 1/72
= 3/72 + 2/72 + 1/72
= (3 + 2 + 1)/72
= 6/72
= 1/12
= 12 minutes
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The ratio of the efficiency of pipes P, Q and R are 3 : 2 : 1 respectively and Pipe R can fill the tank in 1 hour 12 minutes. Find the time taken by pipes P, Q and R together to fill the tank?a)18 minutesb)24 minutesc)30 minutesd)12 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer?
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