Two taps separately can fill a tank in 10min. and 20 min. respectively. If the taps are opened alternately each for a minute. Find the time taken to fill the tank.

Tap $A fills in 10\min \to 1\min \to {\frac{1}{10}}^{th}part$

Tap $B fills in 20\min \to 1\min \to {\frac{1}{20}}^{th}part$

Together $(A+B) fills in 2\min \to \frac{1}{10}+\frac{1}{20}=\frac{3}{20}$

$6\times 2 min\to in 12 min \frac{6\times 3}{20}=\frac{18}{20} part is filled$

remaining $\frac{2}{20}={\frac{1}{10}}^{th }part is filled by A in 1 minute$

the tank in filled in 12 min+1 min$\to 13 minutes$