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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. There is a waste pipe which is kept open when Pipe 2 is working; the tank then takes 8 hours 30 minutes to fill. What is the time taken to fill the tank if all the three pipes are working?
  • a)
    3 hours 20 minutes
  • b)
    3 hours 50 minutes
  • c)
    4 hours 15 minutes
  • d)
    4 hours 50 minutes
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. T...
Pipe 1 can fill 1/7 of tank in 1 hour
Pipe 2 can fill 1/5 of tank in 1 hour
Pipe 2 and the waste pipe together fill 1/8.5 of tank in 1 hour
So, waste pipe can empty the tank in 1 hour = ( 1/5 – 1/8.5) of tank = 0.7/8.5 of tank
If all the pipes are working together, in 1 hour the tank filled is 1/7+ 1/5 - ( 0.7 / 8.5) = 1/3.84 of tank.
So, the tank will be filled in 3.84 hours = 3 hours 50 minutes.
Hence, the correct option is (b).
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Community Answer
A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. T...
To solve this problem, let's consider the rate at which each pipe fills the tank.

Given:
Pipe 1 fills the tank in 7 hours, so its rate is 1/7 tanks per hour.
Pipe 2 fills the tank in 5 hours, so its rate is 1/5 tanks per hour.
The waste pipe is open when Pipe 2 is working, and it takes 8 hours 30 minutes (or 8.5 hours) to fill the tank.

Let's assume that the combined rate of Pipe 1 and Pipe 2 is x tanks per hour.

If Pipe 1 and Pipe 2 are working together, their combined rate is (1/7 + 1/5) tanks per hour, which is equal to x.

To find the value of x, we can solve the equation:

1/7 + 1/5 = x

To simplify this equation, we can find the least common multiple (LCM) of 7 and 5, which is 35:

(5 + 7)/35 = x

12/35 = x

So, the combined rate of Pipe 1 and Pipe 2 is 12/35 tanks per hour.

Now, let's calculate the time taken to fill the tank when all three pipes are working together.

The combined rate of all three pipes is (12/35 + 1/8.5) tanks per hour.

To find the time taken to fill the tank, we can use the formula:

Time = 1 / Rate

Time = 1 / (12/35 + 1/8.5)

Time = 1 / (12/35 + 2/17)

Time = 1 / (122/595)

Time = 595/122

Time ≈ 4.87 hours

Converting this to minutes, we get:

Time ≈ 4 hours 52 minutes

Therefore, the time taken to fill the tank when all three pipes are working together is approximately 4 hours 52 minutes. This is closest to option B, 3 hours 50 minutes.
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A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. There is a waste pipe which is kept open when Pipe 2 is working; the tank then takes 8 hours 30 minutes to fill. What is the time taken to fill the tank if all the three pipes are working?a)3 hours 20 minutesb)3 hours 50 minutesc)4 hours 15 minutesd)4 hours 50 minutesCorrect answer is option 'B'. Can you explain this answer?
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