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Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.
Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?
- a)25, 14, 15
- b)20, 12, 15
- c)20, 14, 15
- d)25, 12, 15
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Direction: To complete a certain work, C working alone takes twice as...
To solve this problem, let's assign variables to represent the time taken by each person to complete the work individually.
Let's say A takes x days to complete the work alone.
So, B takes x/3 days to complete the work alone.
And C takes 2(x/3) = 2x/3 days to complete the work alone.
We are also given that A and B together can complete the work in 5 days.
So, their combined work rate is 1/5 of the work per day.
Similarly, C takes twice as long as A and B together, so his work rate is half of their combined work rate. Therefore, C's work rate is 1/(5*2) = 1/10 of the work per day.
Now, let's calculate the work rate of A, B, and C individually.
A's work rate = 1/x
B's work rate = 1/(x/3) = 3/x
C's work rate = 1/(2x/3) = 3/(2x)
Since we know that their combined work rate is 1/5, we can add their individual work rates to find the combined work rate:
1/x + 3/x + 3/(2x) = 1/5
Let's solve this equation to find the value of x.
Multiplying the equation by 10x to eliminate the denominators, we get:
10 + 30 + 15 = 2x
55 = 2x
x = 55/2 = 27.5
Therefore, A takes 27.5 days to complete the work alone.
B takes 27.5/3 = 9.17 days to complete the work alone.
C takes 2(27.5/3) = 18.33 days to complete the work alone.
The closest option to these values is option B: 20, 12, 15 days respectively for A, B, and C to complete the work individually.
Let's say A takes x days to complete the work alone.
So, B takes x/3 days to complete the work alone.
And C takes 2(x/3) = 2x/3 days to complete the work alone.
We are also given that A and B together can complete the work in 5 days.
So, their combined work rate is 1/5 of the work per day.
Similarly, C takes twice as long as A and B together, so his work rate is half of their combined work rate. Therefore, C's work rate is 1/(5*2) = 1/10 of the work per day.
Now, let's calculate the work rate of A, B, and C individually.
A's work rate = 1/x
B's work rate = 1/(x/3) = 3/x
C's work rate = 1/(2x/3) = 3/(2x)
Since we know that their combined work rate is 1/5, we can add their individual work rates to find the combined work rate:
1/x + 3/x + 3/(2x) = 1/5
Let's solve this equation to find the value of x.
Multiplying the equation by 10x to eliminate the denominators, we get:
10 + 30 + 15 = 2x
55 = 2x
x = 55/2 = 27.5
Therefore, A takes 27.5 days to complete the work alone.
B takes 27.5/3 = 9.17 days to complete the work alone.
C takes 2(27.5/3) = 18.33 days to complete the work alone.
The closest option to these values is option B: 20, 12, 15 days respectively for A, B, and C to complete the work individually.
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Community Answer
Direction: To complete a certain work, C working alone takes twice as...
Given that, 3 times A’s daily work = (B + C)’s one day’s work.
⇒ (A + B + C)’s daily work = 4 times A’s daily work.
But (A + B+ C)’s daily work = ⅕
⇒ A’s daily work = 1/20, A takes 20 days to do the work.
Also, given 2 times C’s daily work = (A + B)’s daily work
⇒ 3 times C’s daily work = (A + B + C)’s daily work
But (A + B + C)’s daily work = ⅕
⇒ C’s daily work = 1/15, So C takes 15 days to do the work
⇒ B’s daily work = 1/5 – (1/20 + 1/15) = 1/12
⇒ A, B and C working alone can complete the work in 20 days, 12 days and 15 days.
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Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer? for Banking Exams 2024 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Direction: To complete a certain work, C working alone takes twice as long as A and B working together. A working alone takes 3 times as long as B and C working together. All the three together can complete the work in 5 days.Q. How long would each of them i.e. A, B and C take respectively to complete the work individually?a)25, 14, 15b)20, 12, 15c)20, 14, 15d)25, 12, 15e)None of theseCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Banking Exams.
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