15 farmers can cultivate 18 bighas of land in 5 days. Using the concept of inverse variation, find how many days 10 farmers will take to cultivate 12 bighas of land.

Q.15 farmers can cultivate 18 bighas of land in 5 days. Using the concept of inverse variation, find how many days 10 farmers will take to cultivate 12 bighas of land.

Let the number of farmers be \(N\), the number of days be \(D\), and the amount of land cultivated be \(A\). If the amount of land is fixed, increasing the number of days decreases the number of farmers, and vice versa. If the number of days is fixed, increasing the amount of land increases the number of farmers, and vice versa. So, \(N\) and \(D\) are inversely proportional, and \(N\) and \(A\) are directly proportional. Therefore, when both \(A\) and \(D\) vary: \[ N \propto \frac{A}{D} \Rightarrow N = \frac{kA}{D} \quad \text{where } k \text{ is a non-zero constant} \] Given: \(N = 15\), \(D = 5\), and \(A = 18\) \[ 15 = \frac{k \times 18}{5} \Rightarrow k = \frac{15 \times 5}{18} = \frac{25}{6} \] So the general formula becomes: \[ N = \frac{25A}{6D} \quad \text{(i)} \] Now, using equation (i) with \(N = 10\) and \(A = 12\): \[ 10 = \frac{25 \times 12}{6D} \Rightarrow D = \frac{25 \times 12}{6 \times 10} = 5 \] ∴ 10 farmers will take 5 days to cultivate 12 bighas of land.