A and B rent a pasture for 10 months and A puts in 90 cows for 7 months. How many cows can B put in for the remaining 3 months, if he pays half as much as A?

105

Let the rent for one cow = Rs.1/pm

Then, rent for each partners = no. of cows × time

              A     :     B

No.   :   90    :     x

Time :    7     :     3

Rent :  630   :    3x

So ATQ,

B paid half the rent paid by A = \(\frac{630}{2}\) = 315

⇒ 3x = 315

⇒ x = 105

Therefore, B puts in 105 cows for the rest 3 months.