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Three pipes P, Q and R together can fill an empty tank in 16 hours. The ratio between the efficiency of pipe P and Q is 4:3 respectively. Pipe S can empty 70% of the completely filled tank in 28 hours. If pipe R and S together can fill the empty tank in 120 hours, then find out the time taken by pipe Q alone to fill 55% of the tank.
  • a)
    28 hours
  • b)
    44 hours
  • c)
    56 hours
  • d)
    32 hours
  • e)
    None of the above
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Three pipes P, Q and R together can fill an empty tank in 16 hours. T...
Pipe S can empty 70% of the completely filled tank in 28 hours.
Time taken by pipe S to empty the completely filled tank = 28 of (10/7)
= 40 hours
Let’s assume the total capacity of the tank is 480 units.
Efficiency of pipe S = 480/40 = -12 units/hour (Here negative sign represents emptying the tank.)
pipe R and S together can fill the empty tank in 120 hours.
Total efficiency of pipe R and S = 480/120 = 4 units/hour
Efficiency of pipe R = 16 units/hour
Three pipes P, Q and R together can fill an empty tank in 16 hours.
Efficiency of pipes P, Q and R together = 480/16 = 30 units/hour
Efficiency of pipes P and Q together = 30-16 = 14 units/hour
The ratio between the efficiency of pipe P and Q is 4:3 respectively.
Efficiency of pipe P = 14 of (4/7) = 8 units/hour
Efficiency of pipe Q = 14 of (3/7) = 6 units/hour
time taken by pipe Q alone to fill 55% of the tank = 55% of (480/6)
= 55% of 80
= 44 hours
Free Test
Community Answer
Three pipes P, Q and R together can fill an empty tank in 16 hours. T...
Let's solve this problem step by step:

Step 1: Find the individual efficiencies of pipes P and Q.
Let the efficiency of pipe P be 4x and the efficiency of pipe Q be 3x.
Therefore, the total efficiency of pipes P and Q together is 4x + 3x = 7x.

Step 2: Find the efficiency of pipe S.
Pipe S can empty 70% of the completely filled tank in 28 hours. Let the efficiency of pipe S be y.
Therefore, the efficiency of pipe S is 70% of the efficiency required to fill the tank in 1 hour.
So, the efficiency of pipe S is (100/28)% of the efficiency required to fill the tank in 1 hour, which is (100/28)y.

Step 3: Find the combined efficiency of pipes R and S.
Pipe R and S together can fill the empty tank in 120 hours. Let the efficiency of pipe R be z.
Therefore, the combined efficiency of pipes R and S is (1/120) of the efficiency required to fill the tank in 1 hour, which is (1/120)(z + (100/28)y).

Step 4: Find the combined efficiency of all three pipes P, Q, and R.
The combined efficiency of pipes P, Q, and R is 1/16 of the efficiency required to fill the tank in 1 hour, which is (1/16)(4x + 3x + z).

Step 5: Equate the combined efficiencies of pipes P, Q, and R, and pipes R and S.
Since the combined efficiencies are equal, we can set the equations equal to each other:
(1/16)(4x + 3x + z) = (1/120)(z + (100/28)y)

Step 6: Simplify and solve the equation.
Simplifying the equation, we get:
7x + z = (100/28)y

Step 7: Find the ratio of the efficiencies of pipes P, Q, and R.
Since the ratio between the efficiency of pipe P and Q is 4:3, we can equate the efficiencies:
4x = (3/4)(7x)
16x = 21x
x = 0

Step 8: Determine the value of x from the given information.
Since x = 0, it means that the efficiency of pipes P and Q is 0. This cannot be true, so there must be an error in the given information.

Step 9: Conclusion
Based on the given information, it is not possible to determine the time taken by pipe Q alone to fill 55% of the tank. The correct answer should be "None of the above" as the information provided is inconsistent.
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Three pipes P, Q and R together can fill an empty tank in 16 hours. The ratio between the efficiency of pipe P and Q is 4:3 respectively. Pipe S can empty 70% of the completely filled tank in 28 hours. If pipe R and S together can fill the empty tank in 120 hours, then find out the time taken by pipe Q alone to fill 55% of the tank.a)28 hoursb)44 hoursc)56 hoursd)32 hourse)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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