A takes 10 days less than the time taken by B to finish a piece of work. If both A and B can do it in 12 days, then the time taken by B alone to finish the work is = ?

Solution(By Examveda Team)

Let B can alone finish the work = x days
So, A can alone finish the work = (x - 10) days
Now, one day work of A = $$\frac{1}{{{\text{x}} - 10}}$$
and one day work of B = $$\frac{1}{{\text{x}}}$$
Now, given (A + B) can finish the work = 12 day
So, one day work of (A + B) = $$\frac{1}{{12}}$$
$$\eqalign{ & \Rightarrow \frac{1}{{{\text{x}} - 10}} + \frac{1}{{\text{x}}} = \frac{1}{{12}} \cr & \Rightarrow \frac{{x + x - 10}}{{x \times \left( {x - 10} \right)}} = \frac{1}{{12}} \cr & \Rightarrow \frac{{2x - 10}}{{{x^2} - 10x}} = \frac{1}{{12}} \cr & \Rightarrow 12\left( {2x - 10} \right) = {x^2} - 10x \cr & \Rightarrow 24x - 120 = {x^2} - 10x \cr & \Rightarrow {x^2} - 10x - 24x + 120 = 0 \cr & \Rightarrow {x^2} - 34x + 120 = 0 \cr & \Rightarrow {x^2} - 30x - 4x + 120 = 0 \cr & \Rightarrow x\left( {x - 30} \right) - 4\left( {x - 30} \right) = 0 \cr & \Rightarrow \left( {x - 30} \right) \times \left( {x - 4} \right) = 0 \cr & \Rightarrow x = 30,\,4 \cr} $$
if x = 4, then A alone can finish the work = 4 - 10 = -6, which is not possible.
So, x = 30
Hence, B can alone finish the work = 30 days