Let \(N\) be the number of farmers, \(D\) be the number of days, and \(A\) be the area of cultivated land.
Since keeping the land area constant, increasing (or decreasing) the number of days decreases (or increases) the number of farmers, and keeping the number of days constant, increasing (or decreasing) the land area increases (or decreases) the number of farmers.
Thus, \(N\) and \(D\) are inversely proportional, while \(N\) and \(A\) are directly proportional.
So, \(N∝\cfrac{1}{D}\) when \(A\) is constant,
and \(N∝A\) when \(D\) is constant.
That is, \(N∝\cfrac{A}{D}\) when both \(A\) and \(D\) are variable.
\(∴N=\cfrac{kA}{D}\) [\(k\) = nonzero proportionality constant]
For \(N=15\), \(D=5\), and \(A=18\),
\(15= \cfrac{k×18}{5}\)
or, \(k=\cfrac{15×5}{18}=\cfrac{25}{6}\)
\(∴ N=\cfrac{25A}{6D}-----(i)\)
Substituting \(N=10\) and \(A=12\) in equation (i),
\(10= \cfrac{25×12}{6D}\)
or, \(D=\cfrac{25×12}{6×10}\)
\(∴ D=5\)
∴ 10 farmers will take 5 days to cultivate 12 bighas of land.