A and B together can do a piece of work in 6 days. Whereas A alone can do the same work in 9 days. Then B alone will do same work in:

1. 15 days

2. 6 days

3. 18 days

4. 54 days

18 days

Reason

Given,

A alone can do the same work in 9 days.

So, one day work of A = $\dfrac{1}{9}$

Let B alone can do the same work in y days.

So, one day work of B = $\dfrac{1}{y}$

As together they can do work in 6 days.

∴ In one day, both of them do $\dfrac{1}{6}$th part of work.

$∴ \dfrac{1}{9} + \dfrac{1}{y} = \dfrac{1}{6}\\[1em] \Rightarrow \dfrac{1 \times y}{9\times y} + \dfrac{1\times 9}{y\times 9} = \dfrac{1}{6}\\[1em] \Rightarrow \dfrac{y}{9y} + \dfrac{9}{9y} = \dfrac{1}{6}\\[1em] \Rightarrow \dfrac{y + 9}{9y} = \dfrac{1}{6}\\[1em] \Rightarrow 6(y + 9) = 9y\\[1em] \Rightarrow 6y + 54 = 9y\\[1em] \Rightarrow 9y - 6y = 54\\[1em] \Rightarrow 3y = 54\\[1em] \Rightarrow y = \dfrac{54}{3}\\[1em] \Rightarrow y = 18$

∴ B alone can complete the work in 18 days.

Hence, option 3 is the correct option.