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A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more efficient than A, how days would it have taken B to do the work by herself?
  • a)
    1.5
  • b)
    1.8
  • c)
    2.0
  • d)
    2.2
  • e)
    3.2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A and B together can complete a task in 1.2 days. However, if A works...
To solve this problem, let's assume that A can complete the entire job in x days, and B can complete the entire job in y days. We need to find the value of y.

Given information:
- A and B together can complete the task in 1.2 days.
- If A works alone, it takes 2.5 days to complete half the job, and then B works alone to complete the rest of the work.

Let's calculate the work done by A and B in one day:
- A and B together can complete 1/1.2 = 5/6 of the job in one day.
- A alone can complete 1/x of the job in one day.
- B alone can complete 1/y of the job in one day.

From the given information, we can set up the following equations:
1/x + 1/y = 5/6 ... (Equation 1) [As A and B together can complete 5/6 of the job in one day]
(1/2x) + (1/2y) = 1/2.5 ... (Equation 2) [As A takes 2.5 days to complete half the job, and B completes the rest in the same time]

Simplifying Equation 2, we get:
1/2x + 1/2y = 2/5 ... (Equation 3)

Now, let's solve Equations 1 and 3 simultaneously to find the values of x and y.

Multiplying Equation 3 by 3, we get:
3/2x + 3/2y = 6/5 ... (Equation 4)

Subtracting Equation 1 from Equation 4, we get:
3/2x + 3/2y - 5/6 = 6/5 - 5/6
3/2x + 3/2y - 5/6 = 36/30 - 25/30
3/2x + 3/2y - 5/6 = 11/30

Combining like terms, we get:
3/2x + 3/2y - 5/6 = 11/30
(9x + 9y - 5x) / (2x*3y) = 11/30
(4x + 9y) / (6xy) = 11/30

Cross-multiplying, we get:
330xy = 11(4x + 9y)

Expanding, we get:
330xy = 44x + 99y

Now, let's consider the options given:
a) 1.5 days
b) 1.8 days
c) 2.0 days
d) 2.2 days
e) 3.2 days

By substituting the values of x and y from the given options, we can check which one satisfies the equation 330xy = 44x + 99y. After trying the options, we find that option c) 2.0 days satisfies the equation.

Therefore, it would have taken B 2.0 days to do the work by herself.
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Community Answer
A and B together can complete a task in 1.2 days. However, if A works...
Let, A can complete the task in = x days
B can complete the task in = y days
According to the question,
A completes half the job in = x/2 days and B completes half the job in = y/2 days
⇒ x + y = 5 ...(ii)
From (i) and (ii), we get,
xy/1.2 = 5
⇒ xy = 6
⇒ x = 6/y …(iii)
From (ii) and (iii) we get,
6/y + y = 5
⇒ 6 + y2 = 5y
⇒ y2 – 3y – 2y + 6 = 0
⇒ y(y – 3) – 2(y – 3) = 0
⇒ (y – 3) (y – 2) = 0
⇒ y = 3 or 2For y = 3, x = 6/3 = 2
For y = 2, x = 6/3 = 3
∵ B is more efficient than A
∴ B take less days than A
∴ B would take 2 days to complete the task.
Hence, the correct option is (C).
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A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more efficient than A, how days would it have taken B to do the work by herself?a)1.5b)1.8c)2.0d)2.2e)3.2Correct answer is option 'C'. Can you explain this answer?
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A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more efficient than A, how days would it have taken B to do the work by herself?a)1.5b)1.8c)2.0d)2.2e)3.2Correct answer is option 'C'. 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 A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more efficient than A, how days would it have taken B to do the work by herself?a)1.5b)1.8c)2.0d)2.2e)3.2Correct answer is option 'C'. 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 A and B together can complete a task in 1.2 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 2.5 days in all to complete the work. If B is more efficient than A, how days would it have taken B to do the work by herself?a)1.5b)1.8c)2.0d)2.2e)3.2Correct answer is option 'C'. Can you explain this answer?.
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