Joe went to a shop to buy some Leather and Plastic balls. Leather balls cost Rs 300 each while Plastic balls cost Rs.400 each. Joe spent a total of Rs.3600 on the balls. If he had bought as many Plastic balls as the number of Leather balls he actually bought and vice versa, he would have saved an amount equal to half the cost of one ball of one of the two types. Find the total number of leather balls he actually bought. a. 6 b. 4 c. 3 d. 10

Let's denote the number of leather balls Joe bought as L and the number of plastic balls as P.

From the problem, we know that:

1. The total cost of the balls is Rs.3600, so 300L + 400P = 3600.

2. If Joe had bought as many plastic balls as the number of leather balls he actually bought and vice versa, he would have saved an amount equal to half the cost of one ball of one of the two types. This means that the difference between the cost of the balls he bought and the cost of the balls he could have bought is either half the cost of a leather ball (150) or half the cost of a plastic ball (200). So, we have two possible equations:

   a) 300P + 400L = 3600 - 150, or b) 300P + 400L = 3600 - 200.

Solving these equations, we find that:

For equation a) we get L = 10 and P = 3, which is not possible because P should be greater than L.

For equation b) we get L = 6 and P = 6, which is also not possible because L should not be equal to P.

Therefore, the problem does not have a solution that fits the conditions given. The total number of leather balls he actually bought cannot be determined from the information provided.