Question : The ratio of acid and water in the three samples is 2 : 1, 3 : 2, and 5 : 3. A mixture containing equal quantities of all three samples is made. The ratio of acid and water in the mixture is:
Option 1: 120 : 133
Option 2: 227 : 133
Option 3: 227 : 120
Option 4: 133 : 227
Correct Answer: 227 : 133
Solution :
Given: The ratio of acid and water in three samples is 2 : 1, 3 : 2, and 5 : 3.
Proportion of acid in 3 samples are $\frac{2}{3},\frac{3}{5},$ and $\frac{5}{8}$.
Total proportion of acid = $\frac{2}{3}+\frac{3}{5}+\frac{5}{8}$ = $\frac{80+72+75}{120}$ = $\frac{227}{120}$
Proportion of water in 3 samples are $\frac{1}{3},\frac{2}{5},$ and $\frac{3}{8}$.
Total proportion of water = $\frac{1}{3}+\frac{2}{5}+\frac{3}{8}=\frac{40+48+45}{120}=\frac{133}{120}$
So, the required ratio = $\frac{\frac{227}{120}}{\frac{133}{120}}$ = 227 : 133.
Hence, the correct answer is 227 : 133.
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