A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Options

  1. 5 : 3
  2. 4 : 5
  3. 5 : 4
  4. 3 : 5

Correct Answer

3 : 5

Explanation

Let the original solution contain: Acid = A litres Water = W litres Step 1: After adding 2 litres of water Total solution = A + (W + 2) litres Acid concentration = 50% → A / (A + W + 2) = 1/2 ⇒ 2A = A + W + 2 ⇒ A − W = 2 … (1) Step 2: After adding 15 litres of acid Total acid = A + 15 Total solution = A + 15 + W + 2 = A + W + 17 Acid concentration = 80% → (A + 15) / (A + W + 17) = 4/5 ⇒ 5(A + 15) = 4(A + W + 17) ⇒ 5A + 75 = 4A + 4W + 68 ⇒ A − 4W = −7 … (2) Step 3: Solve the system of equations From (1): A − W = 2 ⇒ A = W + 2 Substitute into (2): (W + 2) − 4W = −7 ⇒ −3W + 2 = −7 ⇒ −3W = −9 ⇒ W = 3 Then A = W + 2 = 5 Step 4: Ratio of water to acid W : A = 3 : 5

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