1.

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

Answer»

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.


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