PSLE
Fanny bought some lollipops and gave half of it to Julian. Julian bought some chocolate bars and gave half of it to Fanny. Fanny ate 5 chocolate bars and Julian ate 10 lollipops. The ratio of Fanny's chocolate bars to lollipops became 1 : 6 and the ratio of Julian's chocolate bars to lollipops became 1 : 2. How many chocolate bars did Julian buy?

	Fanny		Julian
	Chocolate bars	Lollipops	Chocolate bars	Lollipops
Before	1 u + 5	6 u	1 p	2 p + 10
Change	- 5			- 10
After	1 u	6 u	1 p	2 p

After Fanny gave half of the lollipops to Julian and Julian gave half of his chocolate bars to Fanny, Julian and Fanny had same number of chocolate bars and lollipops before each ate some.

6 u = 2 p + 10 
6 u - 10 = 2 p --- (1)

1 u + 5 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 10 = 2 p --- (3)

(1) = (3)
6 u - 10 = 2 u + 10 
6 u - 2 u = 10 + 10
4 u = 20

1 u = 20 ÷ 4 = 5

1 p
= 1 u + 5
= 5 + 5
= 10

Number of chocolate bars that Julian bought
= 2 p
= 2 x 10
= 20

Answer(s): 20