KarishmaB : hi , i tried the following approach : since 100% pure water is added to the mixture as the 2nd liquid , we can trace the concenteration of sugar since its final / avg. concentration ( 7.5%) is given , initial (55%) we know and 2nd concentration can be assumed as 0% . Thus tracing the sugar concentrations across : 0% - 7.5% - 55% = this gives us the ratio in which water and the mixture shud be combined = 19 : 3 > out of 1 gallon, 3 / 22 gallon is the mixture > out of which 44% is dye thus 3/50 gallon is dye > 3/50 * 100 = 6% of the 1 gallon is the dye. confirming if any logic used here errornous and shudnt be used as we are speaking of not using the scale method.
Have tried writing the explanation in short. incase , not clear , i ll make a step by step flow.
KarishmaB
Responding to a pm:
You have 3 elements here - dye, sugar and water. So we cannot use the scale method.
We see that sugar is 5/9 of the drink and 7.5% of the entire water solution.
Dye which is 4/9 of the drink would be (7.5/5)*4 = 6% of the entire water solution
Answer (A)