There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for the water tank (initially full) to become empty if T2 is opened while T1 is closed is ____________.

Let us assume the tank's capacity to be 60 litres.

If only tap T1 is opened, the tank will empty in 30 minutes. Thus, the draining efficiency of tap T1 is 2 litres per minute.

If both taps, T1 and T2, are opened, then the tank gets empty in 20 minutes. Thus, the combined draining efficiency of taps T1 and T2 is 3 litres per minute.

Thus, the draining efficiency of tap T2 will be 1 litre per minute.

The time required to empty the water tank by tap T2 alone is = $$\dfrac{60\ litre}{1\ litre\ per\ \min}$$ = $$60 min$$