Two taps 'a' and 'b' can fill a water tank in 9min and 12 min respectively.In what time it will be full, if 'b' starts working 2 min after 'a' starts working?...........
Let T denote the volume of the tank.
Then a delivers $\displaystyle \dfrac T9$ per minute and
b delivers $\displaystyle \dfrac T{12}$ per minute.
After x minutes the tank is filled:
$\displaystyle \dfrac T9 \cdot x + \dfrac T{12} \cdot (x-2)=T$ . Divide by T, expand the brackets, collect like terms:
$\displaystyle \dfrac x9 + \dfrac x{12} - \dfrac16=1~\implies~\dfrac7{36} x=\dfrac76~\implies~\boxed{x=6}$