SSC Quantitative Aptitude Mixture And Alligation Question Bank Mixture and Allegation (I)

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

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