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A container is completely filled with a sugar solution composed of water and sugar syrup in the ratio of 7:3. The container has 2 holes covered with filters such that from one of the holes only sugar syrup can flow out and from the other hole only water can flow out. The rates of water outflow and sugar syrup outflow from their respective holes are x cubic centimeters per hour and y cubic centimeters per half an hour respectively, such that x:y = 5:1. If the water from the solution can be drained out completely in 14 hours from the hole, how much time in hours would it take the container to be empty if both the holes are opened simultaneously?
  • a)
    14
  • b)
    15
  • c)
    29
  • d)
    30
  • e)
    44
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A container is completely filled with a sugar solution composed of wat...
Given:
  • Let the volume of the container be S liters
  • Since the container is completely filled with the sugar solution, the volume of sugar solution will also be S liters
    • Volume of water = 0.7S
    • Volume of sugar syrup = 0.3S
  • Rate of water outflow = x cubic centimeters per hour
    • Water can be drained out completely in 14 hours
  • Rate of sugar syrup outflow = y cubic centimeters per half an hour
    • Rate of sugar syrup outflow = 2y cubic centimeters per hour x: y = 5:1
To Find: Time taken for container to be empty, if both the holes are opened simultaneously?
Approach:
  1. As both the holes are opened simultaneously, the time taken to empty the container = Max( Time taken for sugar syrup to drain completely, Time taken for water to drain completely)
  2. So, we need to find the individual time taken for both water and sugar syrup to drain out completely
    • As we are given the time taken for water to drain out completely, we need to find the time taken for sugar syrup to drain out completely
  3. Time taken for sugar syrup to drain completely = 
    • So, we need to find either the values of S and y or the ratio S/Y
  4. Now, we are given that x : y = 5: 1, so if we can find the ratio of S/X, we can find the ratio of S/Y
  5. Also, since we know that water can be drained out completely in 14 hours, we can calculate the ratio of S/X by using
Working out:
 
4. So, let’s compare the time taken for water and sugar syrup to drain out completely
a. Time taken for water to drain out completely = 14 hours
b. Time taken for sugar syrup to drain out completely = 15 hours
5. Hence, the time taken for the container to be empty = Max( 14, 15) = 15 hours
Therefore, the container would be completely empty in 15 hours
Answer B
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A container is completely filled with a sugar solution composed of water and sugar syrup in the ratio of 7:3. The container has 2 holes covered with filters such that from one of the holes only sugar syrup can flow out and from the other hole only water can flow out. The rates of water outflow and sugar syrup outflow from their respective holes are x cubic centimeters per hour and y cubic centimeters per half an hour respectively, such that x:y = 5:1. If the water from the solution can be drained out completely in 14 hours from the hole, how much time in hours would it take the container to be empty if both the holes are opened simultaneously?a)14b)15c)29d)30e)44Correct answer is option 'B'. Can you explain this answer?
Question Description
A container is completely filled with a sugar solution composed of water and sugar syrup in the ratio of 7:3. The container has 2 holes covered with filters such that from one of the holes only sugar syrup can flow out and from the other hole only water can flow out. The rates of water outflow and sugar syrup outflow from their respective holes are x cubic centimeters per hour and y cubic centimeters per half an hour respectively, such that x:y = 5:1. If the water from the solution can be drained out completely in 14 hours from the hole, how much time in hours would it take the container to be empty if both the holes are opened simultaneously?a)14b)15c)29d)30e)44Correct answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A container is completely filled with a sugar solution composed of water and sugar syrup in the ratio of 7:3. The container has 2 holes covered with filters such that from one of the holes only sugar syrup can flow out and from the other hole only water can flow out. The rates of water outflow and sugar syrup outflow from their respective holes are x cubic centimeters per hour and y cubic centimeters per half an hour respectively, such that x:y = 5:1. If the water from the solution can be drained out completely in 14 hours from the hole, how much time in hours would it take the container to be empty if both the holes are opened simultaneously?a)14b)15c)29d)30e)44Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A container is completely filled with a sugar solution composed of water and sugar syrup in the ratio of 7:3. The container has 2 holes covered with filters such that from one of the holes only sugar syrup can flow out and from the other hole only water can flow out. The rates of water outflow and sugar syrup outflow from their respective holes are x cubic centimeters per hour and y cubic centimeters per half an hour respectively, such that x:y = 5:1. If the water from the solution can be drained out completely in 14 hours from the hole, how much time in hours would it take the container to be empty if both the holes are opened simultaneously?a)14b)15c)29d)30e)44Correct answer is option 'B'. Can you explain this answer?.
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