Three cartons, A, B and C, contained 274 balls. Oscar added some balls into Carton A and the number of balls in Carton A tripled. He took out half of the number of balls from Carton B and added another 68 balls into Carton C. As a result, the ratio of the number of balls in Carton A, Carton B and Carton C became 12 : 4 : 7. What was the ratio of the number of balls in Carton B to the total number of balls in Carton A and Carton C at first? Give the answer in its lowest term.

	Carton A	Carton B	Carton C	Total
Before	1x4 = 4 u	2x4 = 8 u	7 u - 68	274
Change	+ 2x4 = + 8 u	- 1x4 = - 4 u	+ 68
After	3x4 = 12 u	1x4 = 4 u
Comparing the 3 cartons	12 u	4 u	7 u

The number of balls in Carton A in the end is repeated.  Make the number of balls in Carton A in the end the same. LCM of 3 and 12 is 12.

The number of balls in Carton B in the end is repeated. Make the number of balls in Carton B in the end the same. LCM of 1 and 4 is 4.

Total number of balls at first
= 4 u + 8 u + 7 u - 68
= 19 u - 68

19 u - 68 = 274
19 u = 274 + 68
19 u = 342

1 u = 342 ÷ 19 = 18

Number of balls in Carton B at first
= 8 u
= 8 x 18
= 144

Number of balls in Carton A and Carton C at first
= 274 - 144
= 130

Carton B : Carton A and Carton C
144 : 130 _(÷2)
72 : 65

Answer(s): 72 : 65