In a mixture, the ratio of juice and water is 4 : 3. By adding 6 litre water the ratio of juice and water will be 8 : 7. What is the amount of juice in the original mixture?

Step 1: Let the original quantities of juice and water be 4x and 3x liters respectively.

• This follows from the given ratio 4:3, i.e., Juice : Water = 4x : 3x

Step 2: Add 6 liters of water

• New quantity of water = 3x + 6
• Quantity of juice remains the same = 4x
• New ratio becomes 8:7 ⇒ Juice : Water = 4x : (3x + 6) = 8 : 7

Step 3: Set up the equation

4x / (3x + 6) = 8 / 7

Step 4: Cross-multiply and solve for x

4x × 7 = 8 × (3x + 6)
28x = 24x + 48
28x - 24x = 48
4x = 48
x = 12

Step 5: Calculate original amount of juice

Juice = 4x = 4 × 12 = 48 liters

Answer: 48 liters

There were 48 liters of juice in the original mixture.

This problem demonstrates the use of ratio and proportion in real-world liquid mixture problems. It’s especially useful for aptitude exam practice where such algebraic setup is common. The trick is to assume variables using the given ratio and apply basic algebra to find the unknown quantity.