Explanation

20 people can dig a canal in 15 days
\therefore 1 people can dig a canal in \left(15\times20\right) days
\therefore 30 people can dig a canal in \large\left(\frac{15\times20}{30}\right) days
\rightarrow 10 days
Other side,
To dig a canal in 10 days it will be required 30 people
\therefore To dig a canal in 1 days it will required =\left(30\times10\right) people
\therefore To dig a canal in 6 days it will be required =\large\left(\frac{30\times10}{6}\right) people
\rightarrow 50 people
Ans: 30 people can dig a canal in 10 days and to dig a canal in 6 days it will be required 50 people.

Another way, Rules of Three Method

People and Days are Inversely Proportional.
\therefore\;30\;:\;20\;:\;:\;15\;:\;x
\rightarrow\large\frac{30}{20}=\frac{15}{x}
\rightarrow 30x=20\times15
\rightarrow x=\large\frac{20\times15}{30}
\rightarrow x=10 days
Now,

Days and People are Inversely Proportional.
\therefore\;6\;:\;15\;:\;:\;20\;:\;x
\rightarrow\large\frac{6}{15}=\frac{20}{x}
\rightarrow 6x=15\times20
\rightarrow x=\large\frac{15\times20}{6}
\rightarrow 50 people
Ans: 30 people can dig a canal in 10 days and to dig a canal in 6 days it will be required 50 people.

Additional variations of this particular math query are:

1. If 20 people can dig a canal in 15 days, how many days will it take for 30 people to dig the same canal?
2. How many days will it take for 30 people to dig a canal if it typically takes 20 people 15 days to do so?
3. Given that 20 people can dig a canal in 15 days, how long will it take for 30 people to complete the same task?