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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 theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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?
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.
Substituting this value of a in (i),3c-4b + 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)
156 + 25 - 206 = 362 + 56362+ 106-25 = 06 = 5/3 or-15b 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.
To find:
The time taken by A alone to finish the task.
Let's solve this step by step:
Step 1: Time taken by A, B, and C to finish one-fourth of the task
Let's assume the total time taken by A, B, and C to finish the task is T minutes.
So, the time taken by A, B, and C to finish one-fourth of the task is T/4 minutes.
Given that A, B, and C together take 75 minutes to finish one-fourth of the task, we can write the equation as:
T/4 = 75
Step 2: Time taken by A and B to finish the task
Let's assume the time taken by A and B together to finish the task is X minutes.
So, the time taken by A and C together to finish the task would be 0.75X minutes (75% of X).
Step 3: Time taken by C to finish the task
Given that C takes 300 minutes less than B to finish the task, we can write the equation as:
X - 300 = C
Step 4: Expressing the time taken by A, B, and C to finish the task in terms of X
Since A and C together take 0.75X minutes to finish the task, and C takes X - 300 minutes, we can write the equation as:
0.75X + X - 300 = T
Step 5: Solving the equations
Now, we have two equations:
T/4 = 75
0.75X + X - 300 = T
Let's solve these equations simultaneously.
From the first equation, we can find the value of T:
T = 4 * 75 = 300
Substituting the value of T in the second equation:
0.75X + X - 300 = 300
1.75X = 600
X = 600 / 1.75
X ≈ 342.86
Step 6: Finding the time taken by A alone to finish the task
Since A and B together take X minutes to finish the task, and B takes X - 300 minutes, we can write the equation as:
X = A + X - 300
A = 300
Therefore, the time taken by A alone to finish the task is 300 minutes, which is equivalent to 5 hours or 5 * 60 = 300 minutes.
Hence, the correct answer is option D) 30 hours.
- 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.
To find:
The time taken by A alone to finish the task.
Let's solve this step by step:
Step 1: Time taken by A, B, and C to finish one-fourth of the task
Let's assume the total time taken by A, B, and C to finish the task is T minutes.
So, the time taken by A, B, and C to finish one-fourth of the task is T/4 minutes.
Given that A, B, and C together take 75 minutes to finish one-fourth of the task, we can write the equation as:
T/4 = 75
Step 2: Time taken by A and B to finish the task
Let's assume the time taken by A and B together to finish the task is X minutes.
So, the time taken by A and C together to finish the task would be 0.75X minutes (75% of X).
Step 3: Time taken by C to finish the task
Given that C takes 300 minutes less than B to finish the task, we can write the equation as:
X - 300 = C
Step 4: Expressing the time taken by A, B, and C to finish the task in terms of X
Since A and C together take 0.75X minutes to finish the task, and C takes X - 300 minutes, we can write the equation as:
0.75X + X - 300 = T
Step 5: Solving the equations
Now, we have two equations:
T/4 = 75
0.75X + X - 300 = T
Let's solve these equations simultaneously.
From the first equation, we can find the value of T:
T = 4 * 75 = 300
Substituting the value of T in the second equation:
0.75X + X - 300 = 300
1.75X = 600
X = 600 / 1.75
X ≈ 342.86
Step 6: Finding the time taken by A alone to finish the task
Since A and B together take X minutes to finish the task, and B takes X - 300 minutes, we can write the equation as:
X = A + X - 300
A = 300
Therefore, the time taken by A alone to finish the task is 300 minutes, which is equivalent to 5 hours or 5 * 60 = 300 minutes.
Hence, the correct answer is option D) 30 hours.
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Three persons A, B, and C together have to finish a task. It takes 75 minutesfor them to finish one-fourth of the task. A and C together take 75% of theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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 2025 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 minutesfor them to finish one-fourth of the task. A and C together take 75% of theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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 2025 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 minutesfor them to finish one-fourth of the task. A and C together take 75% of theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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 minutesfor them to finish one-fourth of the task. A and C together take 75% of theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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 2025 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 minutesfor them to finish one-fourth of the task. A and C together take 75% of theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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 2025 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 minutesfor them to finish one-fourth of the task. A and C together take 75% of theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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?.
Solutions for Three persons A, B, and C together have to finish a task. It takes 75 minutesfor them to finish one-fourth of the task. A and C together take 75% of theMarks time taken by A and B together to finish the task. C takes 300 minutes lessthan 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? in English & in Hindi are available as part of our courses for CAT.
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