a) 3 days
b) 9 days
c) 12 days
d) None of these

Answer: d
Explanation:
$$\eqalign{ & {\text{A’s 1 day’s work}} \cr & = \frac{1}{{{\text{T}} + 3}} \cr & {\text{B’s 1 day’s work}} \cr & = \frac{1}{{{\text{T}} + 12}} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{‘s 1 day’s work}} = \frac{1}{{\text{T}}} \cr & \therefore \frac{1}{{{\text{T}} + 3}} + \frac{1}{{{\text{T}} + 12}} = \frac{1}{{\text{T}}} \cr & \Rightarrow \frac{{2{\text{T}} + 15}}{{\left( {{\text{T}} + 3} \right)\left( {{\text{T}} + 12} \right)}} = \frac{1}{{\text{T}}} \cr & \Rightarrow 2{{\text{T}}^2} + 15{\text{T}} = {{\text{T}}^2} + 15{\text{T}} + 36 \cr & {{\text{T}}^2} = 36 \cr & {\text{T}} = 6 \cr} $$