A can complete a task in 6 more days than what B takes to complete the same task. B starts the task and works for 4 days. Then, A alone completes it in 12 days. The time taken (in days) by B alone to complete the same task will be:  

Given:

A can complete a task in 6 more days than B takes to complete the same task.

B works for 4 days, and then A completes the task in 12 days.

Let B's time to complete the task = x days.

Therefore, A's time to complete the task = x + 6 days.

Formula used:

Work done in 1 day = 1 / (time taken to complete the task)

Total work = Work done by B in 4 days + Work done by A in 12 days

Calculation:

Work done by B in 1 day = 1/x

Work done by A in 1 day = 1/(x + 6)

Total work = 1

⇒ Work done by B in 4 days + Work done by A in 12 days = Total work

⇒ (4/x) + (12/(x + 6)) = 1

⇒ 4(x + 6) + 12x = x(x + 6)

⇒ 4x + 24 + 12x = x² + 6x

⇒ x² + 6x - 16x - 24 = 0

⇒ x² - 10x - 24 = 0

⇒ (x - 12)(x + 2) = 0

⇒ x = 12 or x = -2

Since time cannot be negative, x = 12.

∴ The time taken by B alone to complete the task is 12 days.