Two identical pails D and E contained some water. Pail D was ¹₈ filled and Pail E was ¹₉ filled. The ratio of the total mass of Pail D and the water in it to the total mass of Pail E and the water in it was 13 : 12. The total mass of the two pails and the water they contained was 7500 g. What is the mass of an empty pail?
Mass of Pail D and the water inside = 13 u
Mass of Pail E 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 = 7500

1 u = 7500 ÷ 25 = 300

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

Fraction of the water that Pail D had more than Pail E 
= 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 300
= 1200 g

Answer(s): 1200 g