Two identical buckets U and V contained some water. Bucket U was ¹₇ filled and Bucket V was ¹₈ filled. The ratio of the total mass of Bucket U and the water in it to the total mass of Bucket V and the water in it was 13 : 12. The total mass of the two buckets and the water they contained was 5000 g. What is the mass of an empty bucket?
Mass of Bucket U and the water inside = 13 u
Mass of Bucket V 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 = 5000

1 u = 5000 ÷ 25 = 200

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

Fraction of the water that Bucket U had more than Bucket V 
= 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
= 12 u - 7 u
= 5 u
= 5 x 200
= 1000 g

Answer(s): 1000 g