Two identical pails X and Y contained some water. Pail X was ¹₈ filled and Pail Y was ¹₉ filled. The ratio of the total mass of Pail X and the water in it to the total mass of Pail Y and the water in it was 13 : 12. The total mass of the two pails and the water they contained was 5000 g. What is the mass of an empty pail?
Mass of Pail X and the water inside = 13 u
Mass of Pail Y and the water inside = 12 u

Total mass of the two pails and the water inside them
= 13 u + 12 u
= 25 u

25 u = 5000

1 u = 5000 ÷ 25 = 200

Mass of Pail X and the water in it more than mass of Pail Y and the water in it 
= 13 u - 12 u
= 1 u

Fraction of the water that Pail X had more than Pail Y 
= ¹₈ - ¹₉
= ⁹₇₂ - ⁸₇₂
= ¹₇₂ 

¹₇₂ of the water capacity → 1 u
⁸₇₂ of the water capacity → 8 x 1 u = 8 u

Mass of an empty pail
= 12 u - 8 u
= 4 u
= 4 x 200
= 800 g

Answer(s): 800 g