Two identical buckets M and N contained some water. Bucket M was ¹₈ filled and Bucket N was ¹₉ filled. The ratio of the total mass of Bucket M and the water in it to the total mass of Bucket N and the water in it was 11 : 10. The total mass of the two buckets and the water they contained was 5250 g. What is the mass of an empty bucket?
Mass of Bucket M and the water inside = 11 u
Mass of Bucket N 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 = 5250

1 u = 5250 ÷ 21 = 250

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

Fraction of the water that Bucket M had more than Bucket N 
= ¹₈ - ¹₉
= ⁹₇₂ - ⁸₇₂
= ¹₇₂ 

¹₇₂ of the water capacity → 1 u
⁸₇₂ of the water capacity → 8 x 1 u = 8 u

Mass of an empty bucket
= 10 u - 8 u
= 2 u
= 2 x 250
= 500 g

Answer(s): 500 g