Two identical buckets H and J contained some water. Bucket H was ¹₂ filled and Bucket J was ¹₃ filled. The ratio of the total mass of Bucket H and the water in it to the total mass of Bucket J and the water in it was 7 : 6. The total mass of the two buckets and the water they contained was 1690 g. What is the mass of an empty bucket?
Mass of Bucket H and the water inside = 7 u
Mass of Bucket J and the water inside = 6 u

Total mass of the two buckets and the water inside them
= 7 u + 6 u
= 13 u

13 u = 1690

1 u = 1690 ÷ 13 = 130

Mass of Bucket H and the water in it more than mass of Bucket J and the water in it 
= 7 u - 6 u
= 1 u

Fraction of the water that Bucket H had more than Bucket J 
= ¹₂ - ¹₃
= ³₆ - ²₆
= ¹₆ 

¹₆ of the water capacity → 1 u
²₆ of the water capacity → 2 x 1 u = 2 u

Mass of an empty bucket
= 6 u - 2 u
= 4 u
= 4 x 130
= 520 g

Answer(s): 520 g