Two identical pails S and T contained some water. Pail S was ¹₄ filled and Pail T was ¹₅ filled. The ratio of the total mass of Pail S and the water in it to the total mass of Pail T and the water in it was 7 : 6. The total mass of the two pails and the water they contained was 1690 g. What is the mass of an empty pail?
Mass of Pail S and the water inside = 7 u
Mass of Pail T and the water inside = 6 u

Total mass of the two pails and the water inside them
= 7 u + 6 u
= 13 u

13 u = 1690

1 u = 1690 ÷ 13 = 130

Mass of Pail S and the water in it more than mass of Pail T and the water in it 
= 7 u - 6 u
= 1 u

Fraction of the water that Pail S had more than Pail T 
= 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 pail
= 6 u - 4 u
= 2 u
= 2 x 130
= 260 g

Answer(s): 260 g