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A can complete a piece of work in 4 days; B takes double the time taken by A; C takes double the time taken by B; and D takes double the time taken by C. They are paired in groups of two each. The first pair takes two-thirds of the time taken by the second pair to complete the work. Who make up the first pair?  
  • a)
    A and B
  • b)
    A and C
  • c)
    B and C
  • d)
    A and D
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A can complete a piece of work in 4 days; B takes double the time take...
Amounts of work done in one day by A, B, C and D are 1/4, 1/8, 1/16, and 1/32, respectively.
Using options, we note that the pair of B and C does 3/16 of work in one day.
The pair of A and D does  of the work in one day.
Hence, A and D take 32/9 days.
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Community Answer
A can complete a piece of work in 4 days; B takes double the time take...
Given:
A can complete the work in 4 days.
B takes double the time taken by A.
C takes double the time taken by B.
D takes double the time taken by C.

Let's find the time taken by each person to complete the work:

A takes 4 days.
B takes double the time taken by A, so B takes 2 * 4 = 8 days.
C takes double the time taken by B, so C takes 2 * 8 = 16 days.
D takes double the time taken by C, so D takes 2 * 16 = 32 days.

Now, let's consider the pairs of workers:

The first pair takes two-thirds of the time taken by the second pair to complete the work.

Let's assume the first pair completes the work in X days.
So, the second pair will take (2/3)X days to complete the work.

Now, let's calculate the time taken by the first pair:
A takes 4 days, and B takes 8 days. So, together, A and B can complete the work in 4 * 8 / (4 + 8) = 32 / 12 = 8/3 days.

Similarly, let's calculate the time taken by the second pair:
C takes 16 days, and D takes 32 days. So, together, C and D can complete the work in 16 * 32 / (16 + 32) = 512 / 48 = 32/3 days.

According to the given condition, the first pair takes two-thirds of the time taken by the second pair to complete the work. So, X = (2/3) * (32/3) = 64/9 days.

Therefore, the first pair consists of A and D, as they are the only pair that can complete the work in 64/9 days.

Hence, the correct answer is option D) A and D.
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A can complete a piece of work in 4 days; B takes double the time taken by A; C takes double the time taken by B; and D takes double the time taken by C. They are paired in groups of two each. The first pair takes two-thirds of the time taken by the second pair to complete the work. Who make up the first pair?a)A and Bb)A and Cc)B and Cd)A and DCorrect answer is option 'D'. Can you explain this answer?
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