A tank can be filled by a tap in 20 minutes and by another tap in 60 minutes. Both taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will be completely filled in how much time?

20 minutes

Let the total capacity of the tank be 60 units (LCM of 20 and 60).

• First tap fills $60/20 = 3\text{ units/min}$.
• Second tap fills $60/60 = 1\text{ unit/min}$.

Together, they fill:

$3 + 1 = 4\text{ units/min}$

In the first 10 minutes:

$4 \times 10 = 40\text{ units}$

Remaining water:

$60 - 40 = 20\text{ units}$

Now the first tap is closed, so only the second tap works at 1 unit/min.

Time required to fill the remaining 20 units:

$20 \div 1 = 20\text{ minutes}$

Therefore, the tank will be completely filled 20 minutes after the first tap is shut off.