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A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on ?


(CAT 2018)

Correct answer is '10'. Can you explain this answer?
Most Upvoted Answer
A tank is fitted with pipes, some filling it and the rest draining it....
Let the rate of each filling pipe be 'f ' litres/hr and the rate of each draining pipes be 'd' litres/hr

As per the first condition given in the question, Capacity of tank will be = (6f - 5d ) x 6 …(i)

And as per the second condition given in the question, Capacity of tank will be = (5f - 6d ) x 60 …(ii)

Since the capacity of tank is same in both the cases, on equating (i) and (ii), we have

    ► (6f - 5d) x 6 = (5f - 6d) x 60

    ► or, 6f - 5d = 50f - 60d

    ► or, 44f = 55d

    ► or, 4f = 5d

Therefore, f = 1.25d , putting this value in eq. (i),

Capacity of the tank = (6f - 5d ) x 6 = (7.5d - 5d) x 6 = 15d

When 2 filling and 1 draining pipes work simultaneously, the effective rate of filling the tank = (2f - d ),

Now putting f =1.25d in this eq. we have

Effective rate = (2.5d - d ) = 1.5d

Therefore time required to fill the empty tank = 15d / 1.5d = 10 hours.
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Community Answer
A tank is fitted with pipes, some filling it and the rest draining it....
**Problem Analysis:**
- Let's assume that each filling pipe fills the tank at a rate of 'f' units per hour, and each draining pipe drains the tank at a rate of 'd' units per hour.
- We are given two scenarios:
- In the first scenario, when 6 filling pipes and 5 draining pipes are on, the tank fills up completely in 6 hours.
- In the second scenario, when 5 filling pipes and 6 draining pipes are on, the tank fills up completely in 60 hours.
- We need to find the time required for the tank to fill up completely when one draining pipe and two filling pipes are on.

**Solution:**
1. Let's assume that each filling pipe fills the tank at a rate of 'f' units per hour, and each draining pipe drains the tank at a rate of 'd' units per hour.
2. From the given information, we can set up the following equations:
- 6f - 5d = 1 (Equation 1) [In the first scenario, the tank gets filled in 6 hours]
- 5f - 6d = 1/60 (Equation 2) [In the second scenario, the tank gets filled in 60 hours]
3. To find the time required for the tank to fill up completely when one draining pipe and two filling pipes are on, we can set up the following equation:
- 2f - d = 1/t (Equation 3) [Let 't' be the time in hours]
4. Now, we need to solve the system of equations (Equations 1, 2, and 3) to find the value of 't'.
- Multiply Equation 1 by 12 and Equation 2 by 60 to eliminate the fractions:
- 72f - 60d = 12 (Equation 4)
- 300f - 360d = 5 (Equation 5)
- Subtract Equation 5 from Equation 4 to eliminate 'f':
- 72f - 60d - (300f - 360d) = 12 - 5
=> -228f + 300d = 7 (Equation 6)
- Multiply Equation 3 by 300 to eliminate 'd':
- 600f - 300d = 300/t (Equation 7)
- Add Equation 6 and Equation 7 to eliminate 'd':
- (-228f + 300d) + (600f - 300d) = 7 + (300/t)
=> 372f = 7 + (300/t)
- Rearrange the equation:
- 372f = 7 + (300/t)
- Divide both sides by 372:
- f = (7 + (300/t))/372
- Substitute the value of 'f' in Equation 3:
- 2((7 + (300/t))/372) - d = 1/t
- Simplify and rearrange the equation:
- (7 + (300/t))/186 - d = 1/t
- Multiply both sides by 186t to eliminate the fractions:
- 7t + 300 - 186dt = 186
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A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on ?(CAT 2018)Correct answer is '10'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on ?(CAT 2018)Correct answer is '10'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on ?(CAT 2018)Correct answer is '10'. Can you explain this answer?.
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