Billy had three bags of red beans, P, Q and R and the mass of each bag of red beans was in the ratio 5 : 1 : 3. Billy decided to transfer 20% of red beans from Bag P into Bag Q and 60% of red beans from Bag R into Bag Q. Given that the mass of Bag Q was 38 kg in the end, how many kilograms of red beans were transferred into Bag Q?

	P	Q	R
Before	5 u	1 u	3 u
Change 1	- 1 u	+ 1 u
Change 2		+ 1.8 u	- 1.8 u
After	4 u	3.8 u	1.2 u

Mass of red beans transferred from Bag P into Bag Q
= 20% x 5 u
= ²⁰₁₀₀ x 5 u
= 4 u

Mass of red beans transferred from Bag R into Bag Q
= 60% x 3 u
= ⁶⁰₁₀₀ x 3 u
= 1.8 u

Mass of red beans in Bag Q in the end
= 1 u + 1 u + 1.8 u
= 3.8 u

3.8 u = 38 

1 u = 38 ÷ 3.8 = 10

Mass of red beans transferred into Bag Q
= 1 u + 1.8 u
= 2.8 u
= 2.8 x 10
= 28 kg

Answer(s): 28 kg