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A pipe takes 3 hours to fill an empty reservoir to 2/7th of its total capacity. How much time (in hours) more would it take to completely fill the reservoir.
  • a)
    3
  • b)
    4.5
  • c)
    6
  • d)
    7.5
  • e)
    9
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A pipe takes 3 hours to fill an empty reservoir to 2/7th of its total ...
Given:
- Time taken by the pipe to fill the reservoir to 2/7th of its total capacity = 3 hours
To find:
- Time taken to completely fill the reservoir

Approach:
- We can assume that the total capacity of the reservoir is 7x (as 2/7th of the total capacity is filled by the pipe)
- So, the amount of water filled by the pipe in 1 hour = (2x/7)/3 = 2x/21
- Now, to fill the remaining 5x/7th of the reservoir, we need to find the time taken by the pipe

Calculation:
- Let the time taken by the pipe to fill the remaining 5x/7th of the reservoir be t
- Amount of water filled by the pipe in t hours = (2x/21)t
- Total amount of water in the reservoir = 7x
- As the pipe fills 2x/21 amount of water in 1 hour, it will fill 5x/7 amount of water in (5x/7)/(2x/21) = 15/2 hours
- So, the total time taken to fill the reservoir completely = 3 + 15/2 = 21/2 hours

Therefore, the correct answer is option D) 7.5
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Community Answer
A pipe takes 3 hours to fill an empty reservoir to 2/7th of its total ...
Its simple unitary question :
2/7 qty filled in = 3 hrs.
Full qty i.e., 1 will be filled in = 3/ (7/2) = 10.5 hrs.
Extra time required to fill = 10.5 - 3 = 7.5 hrs.
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