Two identical buckets P and Q contained some water. Bucket P was ¹₅ filled and Bucket Q was ¹₆ 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 8 : 7. The total mass of the two buckets and the water they contained was 4500 g. What is the mass of an empty bucket?
Mass of Bucket P and the water inside = 8 u
Mass of Bucket Q 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 = 4500

1 u = 4500 ÷ 15 = 300

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

Fraction of the water that Bucket P had more than Bucket Q 
= 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
= 7 u - 5 u
= 2 u
= 2 x 300
= 600 g

Answer(s): 600 g