A and B can do a piece of work in 12 days, B can C in 8 days and C and A in 6 days. How long would B take to do the same work alone?

Given:

Time taken by A and B to complete the work = 12 days

Time taken by B and C to complete the work = 8 days

Time taken by C and A to complete the work = 6days

Formulae used:

Time = Total work / Efficiency

Calculation:

Let us assume the total work is 1 unit.

$\Rightarrow$ A and B complete 1 unit work in 12 days $\to$ (A and B)'s 1 day's work = $1/12$

$\Rightarrow$ B and C complete 1 unit work in 8 days $\to$ (B and C)'s 1 day's work = 1/ $8$

$\Rightarrow$ A and C complete 1 unit work in 6 days $\to$ (A and C)'s 1 day's work = 1/ $6$

Adding everyone's 1 day's work:

$\Rightarrow 2 (A + B + C) =(1/12 +(1/ 8) +(1/ 6)$

$\Rightarrow A + B + C =9/48$

= A, B, and C's 1 day's work = 9/48

$\Rightarrow$ B's 1 day's work = $(A + B + C) - (A + C)$

$\Rightarrow$ B's 1 day's work =(9/48) $-(1/6) = 9-8 x/48 = 1/ 48$

$\Rightarrow$ B completes 1/ $48$ of the work in 1 day.

Therefore, B alone will take 48 days to complete the work.