Box P and Box Q are identical. ³₄ of Box P and ³₅ of Box Q are filled with sand. The mass of Box Q with its contents is ⁹₁₀ the mass of Box P with its contents. The total mass of the two boxes with their contents is 456 kg. Find the mass of an empty box.
Mass of Box P and its contents = 10 u
Mass of Box Q and its contents = 9 u

Total mass of the two boxes with their contents
= 10 u + 9 u
= 19 u

19 u = 456 

1 u = 456 ÷ 19 = 24

Mass of Box P with its concents more than mass of Box Q with its contents
= 10 u - 9 u
= 1 u
= 1 x 24
= 24 kg

Fraction of the sand that Box P had more than Box Q
= ³₄ - ³₅
= ¹⁵₂₀ - ¹²₂₀
= ³₂₀

³₂₀ of the capacity of sand in a box → 24
¹₂₀ of the capacity of sand in a box → 24 ÷ 3 = 8
¹²₂₀ of the capacity of sand in a box → 12 x 8 = 96 

Mass of the sand and Box Q
= 9 u
= 9 x 24
= 216 kg

Mass of the empty box
= 216 - 96
= 120 kg

Answer(s): 120 kg