Two identical pails D and E contained some water. Pail D was ¹₅ filled and Pail E was ¹₆ 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 10 : 9. The total mass of the two pails and the water they contained was 5130 g. What is the mass of an empty pail?
Mass of Pail D and the water inside = 10 u
Mass of Pail E and the water inside = 9 u

Total mass of the two pails and the water inside them
= 10 u + 9 u
= 19 u

19 u = 5130

1 u = 5130 ÷ 19 = 270

Mass of Pail D and the water in it more than mass of Pail E and the water in it 
= 10 u - 9 u
= 1 u

Fraction of the water that Pail D had more than Pail E 
= ¹₅ - ¹₆
= ⁶₃₀ - ⁵₃₀
= ¹₃₀ 

¹₃₀ of the water capacity → 1 u
⁵₃₀ of the water capacity → 5 x 1 u = 5 u

Mass of an empty pail
= 9 u - 5 u
= 4 u
= 4 x 270
= 1080 g

Answer(s): 1080 g