Two identical pails U and V contained some water. Pail U was ¹₉ filled and Pail V was ¹₁₀ filled. The ratio of the total mass of Pail U and the water in it to the total mass of Pail V and the water in it was 15 : 14. The total mass of the two pails and the water they contained was 8120 g. What is the mass of an empty pail?
Mass of Pail U and the water inside = 15 u
Mass of Pail V and the water inside = 14 u

Total mass of the two pails and the water inside them
= 15 u + 14 u
= 29 u

29 u = 8120

1 u = 8120 ÷ 29 = 280

Mass of Pail U and the water in it more than mass of Pail V and the water in it 
= 15 u - 14 u
= 1 u

Fraction of the water that Pail U had more than Pail V 
= ¹₉ - ¹₁₀
= ¹⁰₉₀ - ⁹₉₀
= ¹₉₀ 

¹₉₀ of the water capacity → 1 u
⁹₉₀ of the water capacity → 9 x 1 u = 9 u

Mass of an empty pail
= 14 u - 9 u
= 5 u
= 5 x 280
= 1400 g

Answer(s): 1400 g