Let the total number of matches played by the team be \(x\).
It is given that the team won \(10\) matches and the winning percentage of the team was \(40\) %.
Therefore,
\(\frac{40}{100}× x = 10\)
\(x = 10 × \frac{100}{40}\)
\(x = 25\)
Thus, the team played \(25\) matches.