Xavier had to paint some boxes. On the first day, the number of boxes he painted was 20% of the number of boxes that he had not painted. One week later, he painted another 30 boxes. As a result, the total number of painted boxes became 10 more than ¹₂ of the total number of boxes. How many less boxes were painted than unpainted on the first day?

	Painted	Not painted	Total
Before	1x1 = 1 u	5x1 = 5 u	6x1 = 6 u
Change	+ 30	- 30
After	1 u + 30	5 u - 30	6 u
Comparing painted and not painted boxes in the end	1x3 + 10 = 3 u + 10	1x3 - 10 = 3 u - 10	2x3 = 6 u

20% = ²⁰₁₀₀ = ¹₅
Painted : Not painted = 1 : 5

The total number of boxes remains unchanged. Make the total number of boxes at first and in the end the same.  LCM of 6 and 2 is 6.

The number of boxes painted in the end is repeated.

3 u + 10 = 1 u + 30
3 u - 1 u = 30 - 10
2 u = 20

1 u = 20 ÷ 2 = 10

Number of less boxes that were painted than not painted on the first day
= 5 u - 1 u
= 4 u
= 4 x 10
= 40

Answer(s): 40