SSC
Quantitative Aptitude
Mixture And Alligation
Question Bank
Mixture and Allegation (II)
question_answer
In a laboratory, two bottles contain mixture of acid and water in the ratio 2 : 5 in the first bottle and 7 : 3 in the second. The ratio in which the contents of these two bottles be mixed such that the new mixture has acid and water in the ratio 2 : 3 is
A)4 : 15
B)9 : 8
C)21 : 8
D)1 : 2
Correct Answer:
C
Solution :
[c]
Acid
Water
Bottle I
\[\frac{2}{7}\]
\[\frac{5}{7}\]
Bottle II
\[\frac{7}{10}\]
\[\frac{3}{10}\]
Let the required ratio be x : 1. Then, according to the question, \[\left( \frac{2}{7}x+\frac{7}{10} \right):\left( \frac{5}{7}x+\frac{3}{10} \right)=2:3\] \[\frac{\frac{2}{7}x+\frac{7}{10}}{\frac{5}{7}x+\frac{3}{10}}=\frac{2}{3}\] \[\Rightarrow \] \[\frac{6}{7}x+\frac{21}{10}=\frac{10}{7}x+\frac{6}{10}\] \[\Rightarrow \] \[\frac{4}{7}x=\frac{15}{10}\]\[\Rightarrow \]\[x=\frac{15}{10}\times \frac{7}{4}=\frac{21}{8}\] Hence, required ratio = x : 1 = 21 : 8