Question

In an 80-litre mixture of milk and water, the ratio of milk to water is 7 : 3. To make this ratio 2 : 1, how many litres of water should be added?

• A. 5 litres
• B. 6 litres
• C. 10 litres
• D. 4 litres

Answer 1

The Correct Option is D

To determine the volume of water required to adjust the milk-to-water ratio from 7:3 to 2:1, implement the following procedure:

1. Initial State: The total mixture volume is 80 litres. The milk to water ratio is 7:3, summing to 10 parts.

2. Initial Volume Calculation:

• Milk quantity: \( \frac{7}{10} \times 80 = 56 \) litres.
• Water quantity: \( \frac{3}{10} \times 80 = 24 \) litres.

3. Target Ratio: The objective is a milk to water ratio of 2:1.

4. Equation Formulation: Let the quantity of water to be added be x litres. The new ratio is represented by:

\[ \frac{56}{24+x} = \frac{2}{1} \]

5. Equation Solution: Solve for x via cross-multiplication:

\( 56 = 2(24 + x) \)

\( 56 = 48 + 2x \)

\( 56 - 48 = 2x \)

\( 8 = 2x \)

\( x = \frac{8}{2} = 4 \)

Consequently, 4 litres of water must be added to achieve the 2:1 ratio.

The required volume is 4 litres.