A and B can separately do a piece of work in 6 days and 12 days respectively. How long will they together take to do the work ?

$(\mathrm{A}+\mathrm{B})$ ’s 1 day’s work $=\frac{1}{6}+\frac{1}{12}=\frac{2+1}{12}=\frac{1}{4}$ ∴ A and B together will complete the work in 4 days. Alternative:

Time taken by A & B together to complete the work.

$=\frac{\text { Total work }}{\text { Efficiency of }(\mathrm{A} \& \mathrm{~B})}$

$=\frac{12}{3}=4$ days