CAT 2001 — QA Question 9

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

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

∴ The pairs are (A, D) and (B, C).

Hence, option (d).