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Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?
- a)60/7
- b)8
- c)30/7
- d)4
- e)A unique answer cannot be determined
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Operating at their respective constant rates, Photocopying machine B t...
Given:
- Time taken by A and B together to copy 7x pages) = 20 minutes
To Find: Time taken by A alone to copy 2x pages
Approach:
2. We’re given the combined output of A and B and the time taken for this output. Using this data, we can find the combined rate of A and B.
Then, we’ll use the equation (Combined Rate of A and B) = (Rate of A) + (Rate of B) to get an equation in terms of a.
Then, we’ll use the equation (Combined Rate of A and B) = (Rate of A) + (Rate of B) to get an equation in terms of a.
Working out:
- When A and B operate simultaneously, 7x pages take 20 minutes
- So, Combined Rate =
pages per minute
- So, Combined Rate =
- The negative root is rejected since time cannot be negative.
- So, a = 4 minutes
- Therefore, Required Time = 2a = 2*4 = 8 minutes
Looking at the answer choices, we see that the correct answer is Option B
Most Upvoted Answer
Operating at their respective constant rates, Photocopying machine B t...
Given information:
- Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages.
- When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes.
To find:
- In how many minutes can machine A operating alone copy 2x pages?
Solution:
Let's say machine A takes t minutes to copy x pages.
Then, machine B takes (t+6) minutes to copy x pages.
When both machines operate simultaneously,
- Machine A can copy (7x/t) pages in 20 minutes.
- Machine B can copy (7x/(t+6)) pages in 20 minutes.
And, the combined output is 7x pages in 20 minutes.
Using the above information, we can form the following equation:
7x/t + 7x/(t+6) = 7x/20
Simplifying the above equation, we get:
t^2 + 6t - 120 = 0
Solving the quadratic equation, we get:
t = 10 or t = -12
Since time cannot be negative, we take t = 10 minutes.
So, machine A can copy x pages in 10 minutes.
Therefore, machine A can copy 2x pages in 20 minutes.
Hence, the answer is option 'B' - 8.
- Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages.
- When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes.
To find:
- In how many minutes can machine A operating alone copy 2x pages?
Solution:
Let's say machine A takes t minutes to copy x pages.
Then, machine B takes (t+6) minutes to copy x pages.
When both machines operate simultaneously,
- Machine A can copy (7x/t) pages in 20 minutes.
- Machine B can copy (7x/(t+6)) pages in 20 minutes.
And, the combined output is 7x pages in 20 minutes.
Using the above information, we can form the following equation:
7x/t + 7x/(t+6) = 7x/20
Simplifying the above equation, we get:
t^2 + 6t - 120 = 0
Solving the quadratic equation, we get:
t = 10 or t = -12
Since time cannot be negative, we take t = 10 minutes.
So, machine A can copy x pages in 10 minutes.
Therefore, machine A can copy 2x pages in 20 minutes.
Hence, the answer is option 'B' - 8.
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Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?a)60/7b)8c)30/7d)4e)A unique answer cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
Question Description
Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?a)60/7b)8c)30/7d)4e)A unique answer cannot be determinedCorrect 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 Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?a)60/7b)8c)30/7d)4e)A unique answer cannot be determinedCorrect 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 Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?a)60/7b)8c)30/7d)4e)A unique answer cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?a)60/7b)8c)30/7d)4e)A unique answer cannot be determinedCorrect 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 Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?a)60/7b)8c)30/7d)4e)A unique answer cannot be determinedCorrect 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 Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?a)60/7b)8c)30/7d)4e)A unique answer cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
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