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Three persons A, B and C are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?
- a)12
- b)10
- c)16
- d)15
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Three persons A, B and C are employed to do a work, person A is 25% m...
Ratio of efficiency of A to B = A: B = 125%: 100% = 5: 4
B's 5 days work = C's 3 days work = 5 * B = 3 * C
B: C = 3: 5
Ratio of efficiency of A, B and C = (5 * 3): (4 * 3): (4 * 5) = 15: 12: 20
Ratio of time taken by A, B and C = (1/15): (1/12): (1/20) = 4: 5: 3
Let time taken by A, B and C is 4x, 5x and 3x respectively.
According to the question-
(1/4x) + (1/3x) = (1/12)
=> x = 7
(4/4x) + (10/5x) + (T/3x) = 1
(1/7) + (2/7) + (T/21) = 1
(T/21) = 1 - (1/7) - (2/7) = (4/7)
T = 12 days
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Community Answer
Three persons A, B and C are employed to do a work, person A is 25% m...
Let's break down the information given in the question:
1. A is 25% more efficient than B: This means that if B takes x days to complete the work, A will take 0.75x days to complete the same work.
2. B takes 5 days to complete the work that C can complete in 3 days: This means that if C takes y days to complete the work, B will take (5/3)y days to complete the same work.
3. A and C together take 12 days to complete the work: This means that if A takes 4 days to complete a part of the work and C takes z days to complete the remaining work, their combined time is 12 days.
Now, let's calculate the values of x, y, and z:
From point 1: A takes 0.75x days to complete the work.
From point 2: B takes (5/3)y days to complete the work.
From point 3: A takes 4 days and C takes z days to complete the work.
Now, using these values, we can calculate the total work done by A, B, and C individually:
Work done by A = 1/(0.75x) * 4 = 4/(0.75x) = 16/(3x)
Work done by B = 1/(5/3)y * 10 = 3/5 * 10/y = 30/y
Work done by C = 1/z * (12 - 4) = 8/z
Since B's work in 5 days is equal to C's work in 3 days, we can equate the two:
30/y = 8/z
Simplifying this equation, we get:
z = 15y/4
Now, since A and C together take 12 days to complete the work, we can equate their work:
16/(3x) + 8/z = 1
Substituting the value of z in terms of y, we get:
16/(3x) + 8/(15y/4) = 1
Simplifying this equation, we get:
16/(3x) + 32/(15y) = 1
Multiplying through by 15xy, we get:
80x + 32x = 15xy
112x = 15xy
Dividing through by x, we get:
112 = 15y
y = 112/15
Substituting this value of y in the equation z = 15y/4, we get:
z = 15(112/15)/4 = 112/4 = 28
Therefore, the value of T is equal to z, which is 28.
Hence, the correct answer is option (A) 12.
1. A is 25% more efficient than B: This means that if B takes x days to complete the work, A will take 0.75x days to complete the same work.
2. B takes 5 days to complete the work that C can complete in 3 days: This means that if C takes y days to complete the work, B will take (5/3)y days to complete the same work.
3. A and C together take 12 days to complete the work: This means that if A takes 4 days to complete a part of the work and C takes z days to complete the remaining work, their combined time is 12 days.
Now, let's calculate the values of x, y, and z:
From point 1: A takes 0.75x days to complete the work.
From point 2: B takes (5/3)y days to complete the work.
From point 3: A takes 4 days and C takes z days to complete the work.
Now, using these values, we can calculate the total work done by A, B, and C individually:
Work done by A = 1/(0.75x) * 4 = 4/(0.75x) = 16/(3x)
Work done by B = 1/(5/3)y * 10 = 3/5 * 10/y = 30/y
Work done by C = 1/z * (12 - 4) = 8/z
Since B's work in 5 days is equal to C's work in 3 days, we can equate the two:
30/y = 8/z
Simplifying this equation, we get:
z = 15y/4
Now, since A and C together take 12 days to complete the work, we can equate their work:
16/(3x) + 8/z = 1
Substituting the value of z in terms of y, we get:
16/(3x) + 8/(15y/4) = 1
Simplifying this equation, we get:
16/(3x) + 32/(15y) = 1
Multiplying through by 15xy, we get:
80x + 32x = 15xy
112x = 15xy
Dividing through by x, we get:
112 = 15y
y = 112/15
Substituting this value of y in the equation z = 15y/4, we get:
z = 15(112/15)/4 = 112/4 = 28
Therefore, the value of T is equal to z, which is 28.
Hence, the correct answer is option (A) 12.
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Three persons A, B and C are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?a)12b)10c)16d)15e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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Three persons A, B and C are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?a)12b)10c)16d)15e)None of theseCorrect answer is option 'A'. 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 are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?a)12b)10c)16d)15e)None of theseCorrect answer is option 'A'. 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 are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?a)12b)10c)16d)15e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
Three persons A, B and C are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?a)12b)10c)16d)15e)None of theseCorrect answer is option 'A'. 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 are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?a)12b)10c)16d)15e)None of theseCorrect answer is option 'A'. 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 are employed to do a work, person A is 25% more efficient than person B and work done by person B in 5 days is equal to the work done by person C in 3 days. Time taken by persons A and C together to finish the work is 12 days. Person A starts working for 4 days, then he is replaced by B who works on it for 10 days, then the remaining part of work is completed by person C alone in 'T' days, then what is the value of 'T'?a)12b)10c)16d)15e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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