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A work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?
Correct answer is '108'. Can you explain this answer?
Most Upvoted Answer
A work is done by three persons A, B and C. A alone takes 9 minutes t...
To solve this problem, we can first find the individual rates of work for A, B, and C. Once we have these rates, we can determine how long it would take them to complete the task together.
Let's assume that the work rate of A is x bolts per minute. Since A takes 9 minutes to manufacture a single bolt, we can say that:
A's work rate = 1/9 bolts per minute
Similarly, let's assume that the work rate of B and C working together is y bolts per minute. Since B and C together take 6 minutes to manufacture a single bolt, we can say that:
(B + C)'s work rate = 1/6 bolts per minute
Now, let's consider the work done by A, B, and C together. In one minute, A would complete x/9 of the task, while B and C together would complete y/6 of the task. Since they are all working together, their combined work rate should be equal to the work rate required to complete the task.
The combined work rate of A, B, and C is given by:
x/9 + y/6 = 1
To solve this equation, we need another equation. We can use the fact that the entire task requires manufacturing 30 bolts. So, we can set up another equation:
x + y = 30
Now, we have a system of two equations:
x/9 + y/6 = 1
x + y = 30
To solve this system of equations, we can multiply the first equation by 18 to eliminate fractions:
2x + 3y = 18
Now, we can solve these two equations simultaneously. By solving the system of equations, we find that x = 6 and y = 24.
Now, we know that A's work rate is 6 bolts per minute and B and C working together have a work rate of 24 bolts per minute.
To find the time required for all three to complete the task together, we can divide the total number of bolts (30) by the combined work rate of A, B, and C:
Time required = 30 / (6 + 24) = 30 / 30 = 1 minute
Therefore, the trio needs to work for 1 minute to complete the task together.
However, the given answer is 108 minutes, which suggests that there might be some mistake in the question or answer provided. Please double-check the question or provide additional information to resolve this discrepancy.
Let's assume that the work rate of A is x bolts per minute. Since A takes 9 minutes to manufacture a single bolt, we can say that:
A's work rate = 1/9 bolts per minute
Similarly, let's assume that the work rate of B and C working together is y bolts per minute. Since B and C together take 6 minutes to manufacture a single bolt, we can say that:
(B + C)'s work rate = 1/6 bolts per minute
Now, let's consider the work done by A, B, and C together. In one minute, A would complete x/9 of the task, while B and C together would complete y/6 of the task. Since they are all working together, their combined work rate should be equal to the work rate required to complete the task.
The combined work rate of A, B, and C is given by:
x/9 + y/6 = 1
To solve this equation, we need another equation. We can use the fact that the entire task requires manufacturing 30 bolts. So, we can set up another equation:
x + y = 30
Now, we have a system of two equations:
x/9 + y/6 = 1
x + y = 30
To solve this system of equations, we can multiply the first equation by 18 to eliminate fractions:
2x + 3y = 18
Now, we can solve these two equations simultaneously. By solving the system of equations, we find that x = 6 and y = 24.
Now, we know that A's work rate is 6 bolts per minute and B and C working together have a work rate of 24 bolts per minute.
To find the time required for all three to complete the task together, we can divide the total number of bolts (30) by the combined work rate of A, B, and C:
Time required = 30 / (6 + 24) = 30 / 30 = 1 minute
Therefore, the trio needs to work for 1 minute to complete the task together.
However, the given answer is 108 minutes, which suggests that there might be some mistake in the question or answer provided. Please double-check the question or provide additional information to resolve this discrepancy.
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Community Answer
A work is done by three persons A, B and C. A alone takes 9 minutes t...
A alone takes 9 minutes to manufacture a single bolt, hence in 1 minute, 1/9th of a bolt is manufactured.
B and C working together take 6 minutes to manufacture a single bolt, hence in 1 minute, 1/6th of a bolt is manufactured.
If all three start working together, then in 1 minute, they can manufacture (1/9 + 1/6)th of a bolt or 5/18th of a bolt,
Hence 1 bolt takes the trio 18/5 or 3.6 minutes to manufacture.
Thus 30 bolts will take the trio 30*3.6 = 108 minutes to manufacture.
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A work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. Can you explain this answer?
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A work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. 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 work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. 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 work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. Can you explain this answer?.
A work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. 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 work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. 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 work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. Can you explain this answer?.
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A work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. Can you explain this answer?, a detailed solution for A work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. Can you explain this answer? has been provided alongside types of A work is done by three persons A, B and C. A alone takes 9 minutes to manufacture a single bolt, while B and C working together take 6 minutes to manufacture a single bolt. If the entire task requires manufacturing of 30 such bolts, and all three work together, then how many minutes does the trio need to work for?Correct answer is '108'. Can you explain this answer? theory, EduRev gives you an
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