Two identical buckets C and D contained some water. Bucket C was ¹₉ filled and Bucket D was ¹₁₀ filled. The ratio of the total mass of Bucket C and the water in it to the total mass of Bucket D and the water in it was 12 : 11. The total mass of the two buckets and the water they contained was 5980 g. What is the mass of an empty bucket?
Mass of Bucket C and the water inside = 12 u
Mass of Bucket D 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 = 5980

1 u = 5980 ÷ 23 = 260

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

Fraction of the water that Bucket C had more than Bucket D 
= 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 260
= 520 g

Answer(s): 520 g