Two identical buckets T and U contained some water. Bucket T was ¹₇ filled and Bucket U was ¹₈ filled. The ratio of the total mass of Bucket T and the water in it to the total mass of Bucket U and the water in it was 10 : 9. The total mass of the two buckets and the water they contained was 3800 g. What is the mass of an empty bucket?
Mass of Bucket T and the water inside = 10 u
Mass of Bucket U and the water inside = 9 u

Total mass of the two buckets and the water inside them
= 10 u + 9 u
= 19 u

19 u = 3800

1 u = 3800 ÷ 19 = 200

Mass of Bucket T and the water in it more than mass of Bucket U and the water in it 
= 10 u - 9 u
= 1 u

Fraction of the water that Bucket T had more than Bucket U 
= ¹₇ - ¹₈
= ⁸₅₆ - ⁷₅₆
= ¹₅₆ 

¹₅₆ of the water capacity → 1 u
⁷₅₆ of the water capacity → 7 x 1 u = 7 u

Mass of an empty bucket
= 9 u - 7 u
= 2 u
= 2 x 200
= 400 g

Answer(s): 400 g