Two identical buckets G and H contained some water. Bucket G was ¹₉ filled and Bucket H was ¹₁₀ filled. The ratio of the total mass of Bucket G and the water in it to the total mass of Bucket H and the water in it was 12 : 11. The total mass of the two buckets and the water they contained was 2760 g. What is the mass of an empty bucket?
Mass of Bucket G and the water inside = 12 u
Mass of Bucket H and the water inside = 11 u

Total mass of the two buckets and the water inside them
= 12 u + 11 u
= 23 u

23 u = 2760

1 u = 2760 ÷ 23 = 120

Mass of Bucket G and the water in it more than mass of Bucket H and the water in it 
= 12 u - 11 u
= 1 u

Fraction of the water that Bucket G had more than Bucket H 
= 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 bucket
= 11 u - 9 u
= 2 u
= 2 x 120
= 240 g

Answer(s): 240 g