According to the formula, if pipe can comletely fill a tank in x hours, then the portion filled in 1 hour is $\frac{1}{x}$

So,

Time taken by A and B together is 6 h $\mathrm{A}+\mathrm{B}=\frac{1}{6}$---Eq 1

Time taken by B and C together is 6 h $\mathrm{B}+\mathrm{C}=\frac{1}{10}$---Eq2

Time taken by C and A together is 6 h $\mathrm{C}+\mathrm{A}=\frac{1}{7{\displaystyle \frac{1}{2}}}=\frac{2}{15}$---Eq3

Adding up all the equations,

$$\begin{gathered} \mathrm{A}+\mathrm{B}+\mathrm{B}+\mathrm{C}+\mathrm{C}+\mathrm{A}=\frac{1}{6}+\frac{1}{10}+\frac{2}{15} \\ 2\mathrm{A}+2\mathrm{B}+2\mathrm{C}=\frac{5+3+4}{30} \\ 2\left(\mathrm{A}+\mathrm{B}+\mathrm{C}\right)=\frac{12}{30} \\ \left(\mathrm{A}+\mathrm{B}+\mathrm{C}\right)=\frac{12}{30\times 2}=\frac{1}{5} \end{gathered}$$

Therefore, pipes A, B and C together can fill the tank in 5 h

∴ $\frac{1}{10}$^th part of the tank will be filled by the pipe in 1 hour.

Hence option D is correct.