The Horse, the Cow and the Sheep

           A man owns a horse, a cow and a sheep. He also owns a pasture.

            If the horse and cow can eat the contents of the pasture in 40 days , while the horse and sheep can do it in 60 days and the cow and the sheep n 90 days, how long all of them together will take to eat all the contents?

Answer:     Since it takes horse the horse and the cow 40 days. In I day  ¹⁄₄₀ of the pasture would be eaten, since it takes the horse and the sheep 60 days, in 1 day ¹⁄₆₀  would be grazed, since it takes the cow and the sheep 90 days, in 1 day ¹⁄₉₀  of the pasture would be devoured.

¹⁄₄₀ + ¹⁄₆₀ + ¹⁄₉₀ = ¹⁹⁄₃₆₀

¹⁹⁄₃₆₀ equals what 2 horses, 2 cows and 2 sheep eat in a day and

¹⁹⁄₃₆₀ ÷ 2 = ¹⁹⁄₇₂₀

¹⁹⁄₇₂₀ equals what 1 horse, 1 cow and 1 sheep eat in 1 day.

 As it takes to eat ¹⁄₇₂₀ of the contents of the pasture ¹⁄₇₂₀ will require 19^th part of 1 day or 720/ 720 or the whole of the contents of the pasture will require 720 times as many days.

Or 37 - ¹⁷⁄₁₉

19: 1: 720: 37 - ¹⁷⁄₁₉