Question

A and B together finish a piece of work in 6 days. If A’s one day’s work is two times that of B, the number of days A and B take to finish the work alone is ____ and ____ respectively.

• A. 9,18
• B. 8,16
• C. 12,24
• D. 7,14

Answer 1

The correct option is A 9,18

If the work done by A in one day is X and that by B is Y, then from the data given:
X + Y $=\frac{1}{6}...\left(i\right)$
$X=2Y...\left(ii\right)$
Thus, (i) $3Y=\frac{1}{6}$
$\Rightarrow Y=\frac{1}{18}...\left(iii\right)$
Thus, B takes 18 days to complete the piece of work alone.
From (ii) and (iii), $X=\frac{1}{9}$.
Thus, A takes 9 days to complete the piece of work alone.