Two identical containers Y and Z contained some water. Container Y was ¹₈ filled and Container Z was ¹₉ filled. The ratio of the total mass of Container Y and the water in it to the total mass of Container Z and the water in it was 13 : 12. The total mass of the two containers and the water they contained was 4000 g. What is the mass of an empty container?
Mass of Container Y and the water inside = 13 u
Mass of Container Z and the water inside = 12 u

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

25 u = 4000

1 u = 4000 ÷ 25 = 160

Mass of Container Y and the water in it more than mass of Container Z and the water in it 
= 13 u - 12 u
= 1 u

Fraction of the water that Container Y had more than Container Z 
= 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 container
= 12 u - 8 u
= 4 u
= 4 x 160
= 640 g

Answer(s): 640 g