Two identical containers U and V contained some water. Container U was ¹₄ filled and Container V was ¹₅ filled. The ratio of the total mass of Container U and the water in it to the total mass of Container V and the water in it was 10 : 9. The total mass of the two containers and the water they contained was 3420 g. What is the mass of an empty container?
Mass of Container U and the water inside = 10 u
Mass of Container V and the water inside = 9 u

Total mass of the two containers and the water inside them
= 10 u + 9 u
= 19 u

19 u = 3420

1 u = 3420 ÷ 19 = 180

Mass of Container U and the water in it more than mass of Container V and the water in it 
= 10 u - 9 u
= 1 u

Fraction of the water that Container U had more than Container V 
= ¹₄ - ¹₅
= ⁵₂₀ - ⁴₂₀
= ¹₂₀ 

¹₂₀ of the water capacity → 1 u
⁴₂₀ of the water capacity → 4 x 1 u = 4 u

Mass of an empty container
= 9 u - 4 u
= 5 u
= 5 x 180
= 900 g

Answer(s): 900 g