It took the villagers 18 days to dig a pond. If the pond is to be dug in 15 days, how many additional people need to be employed? Use the concept of inverse proportion to calculate.

Q.It took the villagers 18 days to dig a pond. If the pond is to be dug in 15 days, how many additional people need to be employed? Use the concept of inverse proportion to calculate.

Let the number of villagers be \(N\) and the number of days be \(D\). Since the total amount of work remains constant, increasing (or decreasing) the number of villagers will decrease (or increase) the number of days. Therefore, \(N\) and \(D\) are inversely proportional. So, \(N ∝ \frac{1}{D}\) ∴ \(N = \frac{k}{D}\), where \(k\) is a non-zero constant. Given: \(N = 50\) when \(D = 18\) So, \(50 = \frac{k}{18}\) ⇒ \(k = 900\) ∴ \(N = \frac{900}{D}\) ———(i) Now, substituting \(D = 15\) in equation (i): \(N = \frac{900}{15} = 60\) ∴ Additional people required = \(60 - 50 = 10\) people.