Let b represent the number of bags of half litre milk and t represent the time required to fill the bags.
Since, the number of bags and time required to fill the bags varies directly.
∴ b ∝ t
∴ b = kt …(i) where k is the constant of variation.
Since, 120 bags can be filled in 3 minutes i.e., when b = 120, t = 3
∴ Substituting b = 120 and t = 3 in (i), we get b = kt
∴ 120 = k × 3
∴ k = 120/3
∴ k = 40
Substituting k = 40 in (i), we get b = kt
∴ b = 40 t …(ii)
This is the equation of variation.
Now, we have to find time required to fill 1800 bags
∴ Substituting b = 1800 in (ii), we get b = 40 t
∴ 1800 = 40 t
∴ t = 1800/40
∴ t = 45
∴ 1800 bags of half litre milk can be filled by the machine in 45 minutes.
