Two identical buckets R and S contained some water. Bucket R was ¹₈ filled and Bucket S was ¹₉ filled. The ratio of the total mass of Bucket R and the water in it to the total mass of Bucket S and the water in it was 13 : 12. The total mass of the two buckets and the water they contained was 5500 g. What is the mass of an empty bucket?
Mass of Bucket R and the water inside = 13 u
Mass of Bucket S and the water inside = 12 u

Total mass of the two buckets and the water inside them
= 13 u + 12 u
= 25 u

25 u = 5500

1 u = 5500 ÷ 25 = 220

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

Fraction of the water that Bucket R had more than Bucket S 
= 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 bucket
= 12 u - 8 u
= 4 u
= 4 x 220
= 880 g

Answer(s): 880 g