Question

120 bags of half litre milk can be filled by a machine within 3 minutes find the time to fill such 1800 bags?

Answer 1

The time required to fill the milk bags varies directly with the time required to fill the bags.

Let the number of minutes be x and the number of bags be y.

Here, x varies directly as y, i.e., x α y.

∴ x = ky, where k is the constant of variation

When x = 3, y = 120

∴ 3 = k × 120

⇒ k = \[\frac{3}{120} = \frac{1}{40}\]

So, the equation of variation is \[x = \frac{1}{40}y\]

When y = 1800,

\[x = \frac{1}{40} \times 1800 = 45\]

Thus, the time required to fill 1800 bags with milk is 45 minutes.