Question: Buffalo produces 10 pounds of milk daily, a cow produces 1 pound of milk daily, and sheep produce 1/4 pound of milk daily.
I need exactly 100 pounds of milk from exactly 100 different animals daily. Also, I should use all 3 types of animals. How do I get it?
Answer:
There are 7 possible answers to it.
Assume that there are B Buffaloes, C Cows and S Sheep.
It is given that a Buffalo produces 10 pounds of milk, a Cow produces 1 pound of mile and a
Sheep produces 0.25 pound of milk. Also, we need 100 pound of milk from exactly 100 animals, we get 2 equations.
10*B + C + 0.25*S = 100 --------- (I)
B + C + S = 100 --------- (II)
Subtracting equation (II) from equation (I)
9*B - 0.75*S = 0
36*B - 3*S = 0 (multiplied by 4)
12*B - S = 0 (division by 3)
12*B = S
Now, for different values of B, we will get multiple solutions.
* 1 Buffalo, 12 Sheep, 87 Cows
* 2 Buffaloes, 24 Sheep, 74 Cows
* 3 Buffaloes, 36 Sheep, 61 Cows
* 4 Buffaloes, 48 Sheep, 48 Cows
* 5 Buffaloes, 60 Sheep, 35 Cows
* 6 Buffaloes, 72 Sheep, 22 Cows
* 7 Buffaloes, 84 Sheep, 9 Cows