A mixture contains acid and water in the ratio of 7 : 4. If 2 liters of water is added to it, then the ratio of acid and water becomes 7 : 5. What is the quantity of acid in the mixture.

a) 14 liters
b) 7 liters
c) 20 liters
d) 21 liters

Ans : a) 14 liters

Solution

Step 1: Define the variables.

Let the initial quantities of acid and water in the mixture be:

• Quantity of acid = ( 7x ) liters
• Quantity of water = ( 4x ) liters

Step 2: Set up the new ratio after adding water.

• After adding 2 liters of water, the quantity of water becomes ( 4x + 2 ) liters.
• The new ratio of acid to water is 7:5, so:
  

Step 3: Solve for ( x ).

Cross-multiply the ratio equation:

Simplify:
35x = 28x + 14
7x = 14
x = 2

Step 4: Calculate the quantity of acid.

• The quantity of acid is ( 7x ).
• Substituting ( x = 2 ):
  Quantity of acid} = 7 x 2 = 14

Answer: The quantity of acid in the mixture is 14 liters.