Two identical buckets A and B contained some water. Bucket A was ¹₅ filled and Bucket B was ¹₆ 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 11 : 10. The total mass of the two buckets and the water they contained was 2100 g. What is the mass of an empty bucket?
Mass of Bucket A and the water inside = 11 u
Mass of Bucket B and the water inside = 10 u

Total mass of the two buckets and the water inside them
= 11 u + 10 u
= 21 u

21 u = 2100

1 u = 2100 ÷ 21 = 100

Mass of Bucket A and the water in it more than mass of Bucket B and the water in it 
= 11 u - 10 u
= 1 u

Fraction of the water that Bucket A had more than Bucket B 
= ¹₅ - ¹₆
= ⁶₃₀ - ⁵₃₀
= ¹₃₀ 

¹₃₀ of the water capacity → 1 u
⁵₃₀ of the water capacity → 5 x 1 u = 5 u

Mass of an empty bucket
= 10 u - 5 u
= 5 u
= 5 x 100
= 500 g

Answer(s): 500 g