Two identical pails X and Y contained some water. Pail X was ¹₃ filled and Pail Y was ¹₄ 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 9 : 8. The total mass of the two pails and the water they contained was 4420 g. What is the mass of an empty pail?
Mass of Pail X and the water inside = 9 u
Mass of Pail Y and the water inside = 8 u

Total mass of the two pails and the water inside them
= 9 u + 8 u
= 17 u

17 u = 4420

1 u = 4420 ÷ 17 = 260

Mass of Pail X and the water in it more than mass of Pail Y and the water in it 
= 9 u - 8 u
= 1 u

Fraction of the water that Pail X had more than Pail Y 
= ¹₃ - ¹₄
= ⁴₁₂ - ³₁₂
= ¹₁₂ 

¹₁₂ of the water capacity → 1 u
³₁₂ of the water capacity → 3 x 1 u = 3 u

Mass of an empty pail
= 8 u - 3 u
= 5 u
= 5 x 260
= 1300 g

Answer(s): 1300 g