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?
Answer & explanation
Correct answer: option 4
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