Ram Singh goes to Pushkar Mela with Rs 10000 to buy exactly 100 animals. He finds that cows are sold at Rs 1000, horses at Rs 300, and chickens at Rs 50. If Ram spends the whole Rs 10000, then what is the maximum number of chickens that he can buy?

Let x,y and z be the number of cows,  horses and chickens, respectively.

Since he has Rs 10,000.

$$1000x+300y+50z$$ = 10,000 ....(I)

$$ x+y+z$$ = 100 ....(II)

300*eqn(II)- eqn(I) gives

$$250z - 700x = 20,000$$

$$z\ =\ \ \frac{\ 20,000+700x}{250}$$

since $$z$$ is an integer then $$Remainder\left(\frac{\ 20,000+700x}{250}\right)$$ = 0

$$Remainder\left(\frac{\ 20,000+700x}{250}\right)$$ = $$Remainder\left(\frac{200x}{250}\right)$$

$$Remainder\left(\frac{200x}{250}\right)$$ = 0 is possible when x takes values 5 ,10, 15 and so on

When x = 5, then z = 94 and y = 1

When x = 10, then z = 108 ( rejected as the total number of animals has to be 100)

For all the values of x greater than 10, the value of z exceeds 100 and does not satisfy the given conditions.

Thus, he has to buy 94 chickens.