Two identical pails X and Y contained some water. Pail X was ¹₂ filled and Pail Y was ¹₃ filled. The ratio of the total mass of Pail X and the water in it to the total mass of Pail Y and the water in it was 6 : 5. The total mass of the two pails and the water they contained was 1650 g. What is the mass of an empty pail?
Mass of Pail X and the water inside = 6 u
Mass of Pail Y and the water inside = 5 u

Total mass of the two pails and the water inside them
= 6 u + 5 u
= 11 u

11 u = 1650

1 u = 1650 ÷ 11 = 150

Mass of Pail X and the water in it more than mass of Pail Y and the water in it 
= 6 u - 5 u
= 1 u

Fraction of the water that Pail X had more than Pail Y 
= 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
= 5 u - 2 u
= 3 u
= 3 x 150
= 450 g

Answer(s): 450 g