Two identical buckets E and F contained some water. Bucket E was ¹₃ filled and Bucket F was ¹₄ filled. The ratio of the total mass of Bucket E and the water in it to the total mass of Bucket F and the water in it was 6 : 5. The total mass of the two buckets and the water they contained was 3190 g. What is the mass of an empty bucket?
Mass of Bucket E and the water inside = 6 u
Mass of Bucket F and the water inside = 5 u

Total mass of the two buckets and the water inside them
= 6 u + 5 u
= 11 u

11 u = 3190

1 u = 3190 ÷ 11 = 290

Mass of Bucket E and the water in it more than mass of Bucket F and the water in it 
= 6 u - 5 u
= 1 u

Fraction of the water that Bucket E had more than Bucket F 
= 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 bucket
= 5 u - 3 u
= 2 u
= 2 x 290
= 580 g

Answer(s): 580 g