A beaker contains acid and water in the ratio 1 : x, when 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid and water becomes 2 : 5. What is the value of x?

2

Quantity of water in 300 ml of mixture = [\(\frac{x}{x + 1}\)] × 300

When 50 ml of water is mixed in the mixture, ratio of acid and water becomes 2 ∶ 5

⇒ Quantity of water in in the new mixture = \(\frac{5}{7}\) × (300 + 50)

⇒ [\(\frac{x}{x + 1}\)] × 300 + 50 = \(\frac{5}{7}\) × (300 + 50)

⇒ [\(\frac{x}{x + 1}\)] × 300 = 250 - 50

⇒ [\(\frac{x}{x + 1}\)] = \(\frac{2}{3}\)

⇒  x = 2