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A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes?
Most Upvoted Answer
A bucket can be filled by two taps in 10 minutes and 15 minutes respec...
Analysis:
To solve this problem, we need to consider the rate at which each tap fills the bucket both with and without obstructions. Let's break down the problem step by step:
Step 1: Calculate the rate of filling the bucket without obstructions
- Let the capacity of the bucket be C.
- The first tap fills the bucket at a rate of C/10 units per minute.
- The second tap fills the bucket at a rate of C/15 units per minute.
Step 2: Calculate the rate of filling the bucket with obstructions
- With obstructions, the first tap fills the bucket at a rate of 2/5 * C/10 = 2C/50 units per minute.
- With obstructions, the second tap fills the bucket at a rate of 3/5 * C/15 = 3C/75 units per minute.
Step 3: Determine the combined rate of filling the bucket with obstructions
- The combined rate of filling the bucket with obstructions is (2C/50) + (3C/75) = 7C/150 units per minute.
Step 4: Calculate the time taken to fill the bucket without obstructions
- The time taken to fill the bucket without obstructions is C / (7C/150) = 150/7 minutes.
Step 5: Calculate the time taken to fill the bucket with obstructions
- The time taken to fill the bucket with obstructions is 12 minutes.
Step 6: Calculate the time for which the taps delivered water with obstructions
- Let x be the time for which the taps delivered water with obstructions.
- Using the concept of work, we can set up the equation: x * (7C/150) = 12 * (C/10 + C/15)
- Solving this equation gives x = 5 minutes.
Therefore, the taps delivered water with obstructions for 5 minutes.
Conclusion:
- The correct answer is (D) 5 minutes.
To solve this problem, we need to consider the rate at which each tap fills the bucket both with and without obstructions. Let's break down the problem step by step:
Step 1: Calculate the rate of filling the bucket without obstructions
- Let the capacity of the bucket be C.
- The first tap fills the bucket at a rate of C/10 units per minute.
- The second tap fills the bucket at a rate of C/15 units per minute.
Step 2: Calculate the rate of filling the bucket with obstructions
- With obstructions, the first tap fills the bucket at a rate of 2/5 * C/10 = 2C/50 units per minute.
- With obstructions, the second tap fills the bucket at a rate of 3/5 * C/15 = 3C/75 units per minute.
Step 3: Determine the combined rate of filling the bucket with obstructions
- The combined rate of filling the bucket with obstructions is (2C/50) + (3C/75) = 7C/150 units per minute.
Step 4: Calculate the time taken to fill the bucket without obstructions
- The time taken to fill the bucket without obstructions is C / (7C/150) = 150/7 minutes.
Step 5: Calculate the time taken to fill the bucket with obstructions
- The time taken to fill the bucket with obstructions is 12 minutes.
Step 6: Calculate the time for which the taps delivered water with obstructions
- Let x be the time for which the taps delivered water with obstructions.
- Using the concept of work, we can set up the equation: x * (7C/150) = 12 * (C/10 + C/15)
- Solving this equation gives x = 5 minutes.
Therefore, the taps delivered water with obstructions for 5 minutes.
Conclusion:
- The correct answer is (D) 5 minutes.
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A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes?
Question Description
A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes?.
A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes?.
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A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes?, a detailed solution for A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes? has been provided alongside types of A bucket can be filled by two taps in 10 minutes and 15 minutes respectively. But due to some obstructions present in both the taps, the former delivers water at two-fifths of its capacity and the latter delivers at three-fifths of its capacity. But after a while the obstructions got removed and the bucket gets filled in 12 minutes from that moment. For how long did the taps deliver water with obstructions present in them? (A), 15 minutes (B) 20 minutes (C) 10 minutes (D) 5 minutes? theory, EduRev gives you an
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