2X+4Y=24

That is x+2y = 12.

2Y= 12-X

Y=6-(？ )X

Since y is a positive integer, 6- (? ) x must be a positive integer,

Therefore, x must be a positive integer multiple of 2,

When x = 2 and y = 5,

When x = 4 and y = 4,

When x = 6 and y = 3,

When x = 8, y = 2.

When x = 10, y = 1.

Because there are fewer chickens than rabbits, only X=2, Y=5 2 and Y = 5 meet the problem.

So, there are two chickens and five rabbits.