Two identical buckets V and W contained some water. Bucket V was ¹₇ filled and Bucket W was ¹₈ filled. The ratio of the total mass of Bucket V and the water in it to the total mass of Bucket W and the water in it was 13 : 12. 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 V and the water inside = 13 u
Mass of Bucket W and the water inside = 12 u

Total mass of the two buckets and the water inside them
= 13 u + 12 u
= 25 u

25 u = 5250

1 u = 5250 ÷ 25 = 210

Mass of Bucket V and the water in it more than mass of Bucket W and the water in it 
= 13 u - 12 u
= 1 u

Fraction of the water that Bucket V had more than Bucket W 
= ¹₇ - ¹₈
= ⁸₅₆ - ⁷₅₆
= ¹₅₆ 

¹₅₆ of the water capacity → 1 u
⁷₅₆ of the water capacity → 7 x 1 u = 7 u

Mass of an empty bucket
= 12 u - 7 u
= 5 u
= 5 x 210
= 1050 g

Answer(s): 1050 g