Billy had three bags of brown rice, V, W and X and the mass of each bag of brown rice was in the ratio 3 : 5 : 2. Billy decided to transfer 10% of brown rice from Bag V into Bag W and 90% of brown rice from Bag X into Bag W. Given that the mass of Bag W was 49.7 kg in the end, how many kilograms of brown rice were transferred into Bag W?

	V	W	X
Before	3 u	5 u	2 u
Change 1	- 0.3 u	+ 0.3 u
Change 2		+ 1.8 u	- 1.8 u
After	2.7 u	7.1 u	0.2 u

Mass of brown rice transferred from Bag V into Bag W
= 10% x 3 u
= ¹⁰₁₀₀ x 3 u
= 2.7 u

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

Mass of brown rice in Bag W in the end
= 5 u + 0.3 u + 1.8 u
= 7.1 u

7.1 u = 49.7 

1 u = 49.7 ÷ 7.1 = 7

Mass of brown rice transferred into Bag W
= 0.3 u + 1.8 u
= 2.1 u
= 2.1 x 7
= 14.7 kg

Answer(s): 14.7 kg