Paul, Billy and Christopher collected marbles in the ratio of 11 : 6 : 7. After Christopher gave ³₅ to Paul and Billy, Christopher had 200 less marbles than Paul. The number of marbles that Billy had increased by 40%. How many marbles did Paul and Christopher have in the end?

	Paul	Billy	Christopher
Before	11 u	6 u	7 u
Change	+ 1.8 u	+ 2.4 u	- 4.2 u
After	12.8 u	8.4 u	2.8 u

Number of marbles that Christopher gave to Paul and Billy
= ³₅ x 7 u
= 4.2 u

Number of marbles that Billy received from Christopher
= ⁴⁰₁₀₀ x 6 u
= 2.4 u

Number of marbles that Paul received from Christopher
= 4.2 u - 2.4 u
= 1.8 u

Number of less marbles that Christopher had less than Paul
= 12.8 u - 2.8 u 
= 10 u

10 u = 200

1 u = 200 ÷ 10 = 20

Number of marbles that Paul and Christopher had
= 12.8 u + 2.8 u
= 15.6 u
= 15.6 x 20
= 312

Answer(s): 312