Owen had three bags of black beans, V, W and X and the mass of each bag of black beans was in the ratio 1 : 4 : 2. Owen decided to transfer 10% of black beans from Bag V into Bag W and 90% of black beans from Bag X into Bag W. Given that the mass of Bag W was 41.3 kg in the end, how many kilograms of black beans were transferred into Bag W?

	V	W	X
Before	1 u	4 u	2 u
Change 1	- 0.1 u	+ 0.1 u
Change 2		+ 1.8 u	- 1.8 u
After	0.9 u	5.9 u	0.2 u

Mass of black beans transferred from Bag V into Bag W
= 10% x 1 u
= ¹⁰₁₀₀ x 1 u
= 0.9 u

Mass of black beans transferred from Bag X into Bag W
= 90% x 2 u
= ⁹⁰₁₀₀ x 2 u
= 1.8 u

Mass of black beans in Bag W in the end
= 4 u + 0.1 u + 1.8 u
= 5.9 u

5.9 u = 41.3 

1 u = 41.3 ÷ 5.9 = 7

Mass of black beans transferred into Bag W
= 0.1 u + 1.8 u
= 1.9 u
= 1.9 x 7
= 13.3 kg

Answer(s): 13.3 kg