Two identical buckets A and B contained some water. Bucket A was ¹₆ filled and Bucket B was ¹₇ filled. The ratio of the total mass of Bucket A and the water in it to the total mass of Bucket B and the water in it was 10 : 9. The total mass of the two buckets and the water they contained was 3610 g. What is the mass of an empty bucket?
Mass of Bucket A and the water inside = 10 u
Mass of Bucket B 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 = 3610

1 u = 3610 ÷ 19 = 190

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

Fraction of the water that Bucket A had more than Bucket B 
= ¹₆ - ¹₇
= ⁷₄₂ - ⁶₄₂
= ¹₄₂ 

¹₄₂ of the water capacity → 1 u
⁶₄₂ of the water capacity → 6 x 1 u = 6 u

Mass of an empty bucket
= 9 u - 6 u
= 3 u
= 3 x 190
= 570 g

Answer(s): 570 g