Two identical pails K and L contained some water. Pail K was ¹₃ filled and Pail L was ¹₄ filled. The ratio of the total mass of Pail K and the water in it to the total mass of Pail L and the water in it was 7 : 6. The total mass of the two pails and the water they contained was 3640 g. What is the mass of an empty pail?
Mass of Pail K and the water inside = 7 u
Mass of Pail L 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 = 3640

1 u = 3640 ÷ 13 = 280

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

Fraction of the water that Pail K had more than Pail L 
= ¹₃ - ¹₄
= ⁴₁₂ - ³₁₂
= ¹₁₂ 

¹₁₂ of the water capacity → 1 u
³₁₂ of the water capacity → 3 x 1 u = 3 u

Mass of an empty pail
= 6 u - 3 u
= 3 u
= 3 x 280
= 840 g

Answer(s): 840 g