Two identical buckets Y and Z contained some water. Bucket Y was ¹₂ filled and Bucket Z was ¹₃ filled. The ratio of the total mass of Bucket Y and the water in it to the total mass of Bucket Z and the water in it was 5 : 4. The total mass of the two buckets and the water they contained was 1890 g. What is the mass of an empty bucket?
Mass of Bucket Y and the water inside = 5 u
Mass of Bucket Z and the water inside = 4 u

Total mass of the two buckets and the water inside them
= 5 u + 4 u
= 9 u

9 u = 1890

1 u = 1890 ÷ 9 = 210

Mass of Bucket Y and the water in it more than mass of Bucket Z and the water in it 
= 5 u - 4 u
= 1 u

Fraction of the water that Bucket Y had more than Bucket Z 
= 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
= 4 u - 2 u
= 2 u
= 2 x 210
= 420 g

Answer(s): 420 g