Two identical pails S and T contained some water. Pail S was ¹₈ filled and Pail T was ¹₉ filled. The ratio of the total mass of Pail S and the water in it to the total mass of Pail T and the water in it was 13 : 12. The total mass of the two pails and the water they contained was 2750 g. What is the mass of an empty pail?
Mass of Pail S and the water inside = 13 u
Mass of Pail T 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 = 2750

1 u = 2750 ÷ 25 = 110

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

Fraction of the water that Pail S had more than Pail T 
= 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 110
= 440 g

Answer(s): 440 g