Two identical buckets T and U contained some water. Bucket T was ¹₄ filled and Bucket U was ¹₅ 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 9 : 8. The total mass of the two buckets and the water they contained was 3400 g. What is the mass of an empty bucket?
Mass of Bucket T and the water inside = 9 u
Mass of Bucket U and the water inside = 8 u

Total mass of the two buckets and the water inside them
= 9 u + 8 u
= 17 u

17 u = 3400

1 u = 3400 ÷ 17 = 200

Mass of Bucket T and the water in it more than mass of Bucket U and the water in it 
= 9 u - 8 u
= 1 u

Fraction of the water that Bucket T had more than Bucket U 
= ¹₄ - ¹₅
= ⁵₂₀ - ⁴₂₀
= ¹₂₀ 

¹₂₀ of the water capacity → 1 u
⁴₂₀ of the water capacity → 4 x 1 u = 4 u

Mass of an empty bucket
= 8 u - 4 u
= 4 u
= 4 x 200
= 800 g

Answer(s): 800 g