Let say $A$ filled $10$ minutes and $B$ filled in $30$ minutes.
Capacity of tank $ = LCM(10,30) = 30$ litre
Efficiency of $A = 3$ litre/minute and efficiency of $B = 1$ litre/minute
Both the taps are kept open for $5$ minutes and then the first one $(A)$ is shut off.
Tank filled by $A\&B$ together for $5$ minute $ = 5\;\text{minute} \times 4 \;\text{litre/minute} = 20$ litre
Tank remaining to be filled $ = 30 – 20 = 10$ litre
Now, only second one $(B),$ filled the tank in $ = \dfrac{10\;\text{litre}}{1 \;\text{litre/minute}} = 10$ minute.
So, the correct answer is $(C).$