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Question:

A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair to complete the work. Which is the first pair?

Explanation:

If A takes 4 days then, B will take 8 days, C will take 16 days and D will take 32 days.

∴ Time taken by A and B together to complete a work $= \frac{(4 \times 8)}{8 + 4} = \frac{8}{3}$ days

∴ Time taken by A and C together to complete a work $= \frac{(4 \times 16)}{16 + 4} = \frac{16}{5}$ days

∴ Time taken by A and D together to complete a work $= \frac{(4 \times 32)}{32 + 4} = \frac{32}{9}$ days

∴ Time taken by A and C together to complete a work $= \frac{(8 \times 16)}{8 + 16} = \frac{16}{3}$ days

$∴ \frac{32}{9} = \frac{2}{3} \times \frac{16}{3}$

∴ The pairs are (A, D) and (B, C).

Hence, option (d).

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