Two identical pails T and U contained some water. Pail T was ¹₂ filled and Pail U was ¹₃ filled. The ratio of the total mass of Pail T and the water in it to the total mass of Pail U and the water in it was 5 : 4. The total mass of the two pails and the water they contained was 2070 g. What is the mass of an empty pail?
Mass of Pail T and the water inside = 5 u
Mass of Pail U and the water inside = 4 u

Total mass of the two pails and the water inside them
= 5 u + 4 u
= 9 u

9 u = 2070

1 u = 2070 ÷ 9 = 230

Mass of Pail T and the water in it more than mass of Pail U and the water in it 
= 5 u - 4 u
= 1 u

Fraction of the water that Pail T had more than Pail U 
= ¹₂ - ¹₃
= ³₆ - ²₆
= ¹₆ 

¹₆ of the water capacity → 1 u
²₆ of the water capacity → 2 x 1 u = 2 u

Mass of an empty pail
= 4 u - 2 u
= 2 u
= 2 x 230
= 460 g

Answer(s): 460 g