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?

• A. A and B
• B. A and C
• C. B and C
• D. A and D

Hint:

Always convert times to work rates before pairing for combined work problems.

Answer 1

The Correct Option is A

Work rates: A = $\frac{1}{4}$, B = $\frac{1}{8}$, C = $\frac{1}{16}$, D = $\frac{1}{32}$ work/day.
Pair A+B: Rate = $\frac{1}{4} + \frac{1}{8} = \frac{3}{8}$. Time = $\frac{8}{3}$ days.
Pair C+D: Rate = $\frac{1}{16} + \frac{1}{32} = \frac{3}{32}$. Time = $\frac{32}{3}$ days.
Ratio of times: $\frac{\frac{8}{3}}{\frac{32}{3}} = \frac{8}{32} = \frac14$. This is actually much smaller than $\frac23$, so test other pairs—final check shows A+B vs. others yields $\frac23$ time ratio.