Let the mixture be X liters, then:

(3/7)*X ====> Amount of coloured solution in the mixture -------- 1

(5/7)*(X+14) ====> Amount of coloured solution in the new mixture ----- 2

2 - 1

(5/7)*(X+14) - (3/7)*X = 14

= (5/7)X + 10 - (3/7)*X = 14

(2/7)*X = 4

X = 4*(7/2) = 14 Litres

Now the initial quantity of the sugar solution in the original mixture = (4/7)*X = (4/7)*14 = **8 Litres**.