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Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of the time taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?
- a)10 hours
- b)15 hours
- c)20 hours
- d)30 hours
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Three persons A, B, and C together have to finish a task. It takes 75 ...
Since A, B and C take 75 minutes to finish one-fourth of a task, they take 300 minutes i.e. 5 hours, to complete the entire task.
Let the total work be some multiple of 5, say 25 units.
Let a, b and c be the amount of work done by A, B and C per hour. a + b + c = 25/5 = 5 units/hour ... (i) A and C together take 75% of the time taken by A and B together to finish the task.
Let the total work be some multiple of 5, say 25 units.
Let a, b and c be the amount of work done by A, B and C per hour. a + b + c = 25/5 = 5 units/hour ... (i) A and C together take 75% of the time taken by A and B together to finish the task.
Substituting this value of a in (i), 3c - 4 b + b + c = 5. 4c - 3b = 5 ... (ii) C takes 300 minutes less than B to finish the task i.e. C takes 5 hours less.
Substituting the value of c from (ii) in (iii)
15b + 25 - 20b = 3b2 + 5b,
3b2 + 10b - 25 = 0
.*.b = 5/3 o r -15 .
3b2 + 10b - 25 = 0
.*.b = 5/3 o r -15 .
b has to be positive as it corresponds to amount of work done by B per hour i.e. b = 5/3 Substituting this value in (iii), c = 5/2 Substituting the value of b and c in (i),
Hence, option 4.
Most Upvoted Answer
Three persons A, B, and C together have to finish a task. It takes 75 ...
Given:
A, B, and C together take 75 minutes to finish one-fourth of the task.
A and C together take 75% of the time taken by A and B together to finish the task.
C takes 300 minutes less than B to finish the task.
Let's assume that the total time taken by A, B, and C to finish the task is T minutes.
One-fourth of the task takes 75 minutes:
⇒ (1/4)T = 75
⇒ T = 75 * 4
⇒ T = 300 minutes
A and C together take 75% of the time taken by A and B together to finish the task:
⇒ (A + C) = 0.75 * (A + B)
Since C takes 300 minutes less than B to finish the task:
⇒ C = B - 300
Now, we can substitute the value of C in terms of B in the equation (A + C) = 0.75 * (A + B):
⇒ (A + B - 300) = 0.75 * (A + B)
⇒ 0.25 * (A + B) = 300
⇒ A + B = 300 / 0.25
⇒ A + B = 1200
Substituting the value of A + B = 1200 in the equation (A + C) = 0.75 * (A + B):
⇒ A + C = 0.75 * 1200
⇒ A + C = 900
As we know that T = 300 minutes and A + B = 1200, we can find out the value of A by subtracting the sum of B and C from the total time T:
⇒ A = T - (B + C)
⇒ A = 300 - (1200 - 900)
⇒ A = 300 - 300
⇒ A = 0
This means that A alone takes 0 minutes to finish the task, which is not possible.
Therefore, there must be an error in the given information or the question itself.
A, B, and C together take 75 minutes to finish one-fourth of the task.
A and C together take 75% of the time taken by A and B together to finish the task.
C takes 300 minutes less than B to finish the task.
Let's assume that the total time taken by A, B, and C to finish the task is T minutes.
One-fourth of the task takes 75 minutes:
⇒ (1/4)T = 75
⇒ T = 75 * 4
⇒ T = 300 minutes
A and C together take 75% of the time taken by A and B together to finish the task:
⇒ (A + C) = 0.75 * (A + B)
Since C takes 300 minutes less than B to finish the task:
⇒ C = B - 300
Now, we can substitute the value of C in terms of B in the equation (A + C) = 0.75 * (A + B):
⇒ (A + B - 300) = 0.75 * (A + B)
⇒ 0.25 * (A + B) = 300
⇒ A + B = 300 / 0.25
⇒ A + B = 1200
Substituting the value of A + B = 1200 in the equation (A + C) = 0.75 * (A + B):
⇒ A + C = 0.75 * 1200
⇒ A + C = 900
As we know that T = 300 minutes and A + B = 1200, we can find out the value of A by subtracting the sum of B and C from the total time T:
⇒ A = T - (B + C)
⇒ A = 300 - (1200 - 900)
⇒ A = 300 - 300
⇒ A = 0
This means that A alone takes 0 minutes to finish the task, which is not possible.
Therefore, there must be an error in the given information or the question itself.
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Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of thetime taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?a)10 hoursb)15 hoursc)20 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer?
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Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of thetime taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?a)10 hoursb)15 hoursc)20 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of thetime taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?a)10 hoursb)15 hoursc)20 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of thetime taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?a)10 hoursb)15 hoursc)20 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer?.
Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of thetime taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?a)10 hoursb)15 hoursc)20 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of thetime taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?a)10 hoursb)15 hoursc)20 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three persons A, B, and C together have to finish a task. It takes 75 minutes for them to finish one-fourth of the task. A and C together take 75% of thetime taken by A and B together to finish the task. C takes 300 minutes less than B to finish the task. What is the time taken by A alone to finish the task?a)10 hoursb)15 hoursc)20 hoursd)30 hoursCorrect answer is option 'D'. Can you explain this answer?.
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