Description for Correct answer:
Let one pipe takes m h to fill the tank.

Then, the other pipe takes \( \Large \left(m-10\right)h \)

According to the question,

Therefore, \( \Large \frac{1}{m}+\frac{1}{ \left(m-10\right) }=\frac{1}{12} \)

=> \( \Large \frac{m-10+m}{m \left(m-10\right) }=\frac{1}{12} \)

=> \( \Large 12 \left(m-10+m\right)=m \left(m-10\right) \)

=> \( \Large m^{2}-34m+120 = 0 \)

=> \( \Large m^{2}-30m-4m+120 = 0 \)

=> \( \Large \left(m-30\right) \left(m-4\right)=0 \)

m = 30 or 4

Faster pipe will take \( \Large \left(30-10\right)h \) = 20 h to fill the tank.