Problem based on Direct and Inverse Variation

35 cattle can graze on a field for 18 days. After 10 days, 15 cattle are move to a different field. For how long can the remaining cattle graze on the field? b) 14.5 days c) 14 days • d) 12 days a) 15 days ​ 

Answer:

If one increases the number of cattle, then the number of days will decrease to graze the same field.

If we increase the number of days, then less cattle will be needed to graze the same field.

So the variables, cattle and number of days are inversely proportional.

Now, if we consider the variables cattle and field size ( keeping the number of days fixed), it is easy to see that they are directly proportional. ( as if you increase the field size, then the number of cattle must be increased to graze in the same day and vice versa)

Let the corresponding quantities for cattle, days and field size be C, D and F.

Then C ∝  ......(i)

⇒C = k , where k is some non-zero constant.

For the initial data, C= 35 and F = 1 ( taking field size as 1 unit ) and D = 18

∴

Now in 1 day, 35 cattle will graze

unit of the field.

Thus in 10 days, they will graze,

unit of the field.

Thus remaining unit of field to be grazed

As 15 cattle were removed, remaining cattle

So the question, boils down to finding the number of days (D) in which 20 cattle (C) will graze

unit (F) of the field.

From (i), C = k

⇒ 

⇒   days

(c) is the correct option