Two identical buckets P and Q contained some water. Bucket P was ¹₈ filled and Bucket Q was ¹₉ filled. The ratio of the total mass of Bucket P and the water in it to the total mass of Bucket Q and the water in it was 12 : 11. The total mass of the two buckets and the water they contained was 3910 g. What is the mass of an empty bucket?
Mass of Bucket P and the water inside = 12 u
Mass of Bucket Q and the water inside = 11 u

Total mass of the two buckets and the water inside them
= 12 u + 11 u
= 23 u

23 u = 3910

1 u = 3910 ÷ 23 = 170

Mass of Bucket P and the water in it more than mass of Bucket Q and the water in it 
= 12 u - 11 u
= 1 u

Fraction of the water that Bucket P had more than Bucket Q 
= 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
= 11 u - 8 u
= 3 u
= 3 x 170
= 510 g

Answer(s): 510 g