Question

Ratio of milk and water in a mixture is 4:3 respectively. If 6 Litres of water is added to this mixture, the respective ratio of milk and water becomes 8:7. What is the quantity of milk in the original mixture?

• A. 96 Litres
• B. 36 Litres
• C. 84 Litres
• D. 48 Litres

Hint:

When a mixture’s ratio changes by adding one component, use algebraic equations to find unknown quantities.

Answer 1

The Correct Option is D

Step 1: Let the quantity of milk = 4x litres and water = 3x litres (since ratio is 4:3)
Step 2: After adding 6 litres water, water quantity = \(3x + 6\) litres
Step 3: New ratio is 8:7 (milk: water)
\[ \frac{4x}{3x + 6} = \frac{8}{7} \] Cross multiply:
\[ 7 \times 4x = 8 \times (3x + 6) \] \[ 28x = 24x + 48 \] \[ 28x - 24x = 48 \] \[ 4x = 48 \] \[ x = 12 \] Step 4: Quantity of milk
\[ 4x = 4 \times 12 = 48 \text{ litres} \] Thus, Option (D) 48 Litres is correct.