A container contained a solution of acid and water, in which water was 64%. Four liters of the solution was taken out of the container and the same quantity of water was added. If the resulting solution contains 30% acid, the quantity of the water in the solution, at the begining in the container was?

15.36

Water : acid 

64% : 36% 

  64 : 36 

  16 : 09

30% acid means ⇒

water : acid 

     7 : 3

ATQ,

⇒ \(\frac{16R - (4 \; ×\frac{16}{25}) \;+\; 4}{9R - (4\; ×\;\frac{9}{25})}\) = \(\frac{7}{3}\)

⇒  \(\frac{16R + \frac{36}{25}}{9R - \frac{36}{25}}\) = \(\frac{7}{3}\)

(Let \(\frac{36}{25}\)) = a

⇒  \(\frac{16R \;+ \; a}{9R - a}\) = \(\frac{7}{3}\)

⇒ 48R + 3a = 63R - 7a

⇒ 15R = 10a

⇒ 3R = 2a

⇒ Put, (\(\frac{36}{25}\)) = a

⇒ 3R = 2 × \(\frac{36}{25}\)

⇒ 1R = \(\frac{24}{25}\)

⇒ Water initially = 16R = 16 × \(\frac{24}{25}\)

⇒ 64 × \(\frac{24}{100}\) = 15.36