Two identical buckets X and Y contained some water. Bucket X was ¹₃ filled and Bucket Y was ¹₄ filled. The ratio of the total mass of Bucket X and the water in it to the total mass of Bucket Y and the water in it was 8 : 7. The total mass of the two buckets and the water they contained was 2550 g. What is the mass of an empty bucket?
Mass of Bucket X and the water inside = 8 u
Mass of Bucket Y and the water inside = 7 u

Total mass of the two buckets and the water inside them
= 8 u + 7 u
= 15 u

15 u = 2550

1 u = 2550 ÷ 15 = 170

Mass of Bucket X and the water in it more than mass of Bucket Y and the water in it 
= 8 u - 7 u
= 1 u

Fraction of the water that Bucket X had more than Bucket Y 
= ¹₃ - ¹₄
= ⁴₁₂ - ³₁₂
= ¹₁₂ 

¹₁₂ of the water capacity → 1 u
³₁₂ of the water capacity → 3 x 1 u = 3 u

Mass of an empty bucket
= 7 u - 3 u
= 4 u
= 4 x 170
= 680 g

Answer(s): 680 g