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 solve the problem of determining how many litres of water should be added to change the milk to water ratio from 7:3 to 2:1, follow these steps: 

1. Initial Composition: The total mixture is 80 litres. The ratio of milk to water is 7:3, which means the parts add up to 10 (7+3).

2. Calculate Initial Quantities:

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

3. Desired Ratio: We want the ratio of milk to water to be 2:1.

4. Establishing Equation: Let x be the litres of water to be added. The new ratio condition is:

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

5. Solve the Equation: Cross-multiply to find x:

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

\( 56 = 48 + 2x \)

\( 56 - 48 = 2x \)

\( 8 = 2x \)

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

Thus, 4 litres of water should be added to make the ratio 2:1.

The correct answer is 4 litres.

Answer 2

Let's break down this problem step-by-step:

1. Initial Quantities:

• Total mixture: 80 litres
• Milk to water ratio: 7 : 3
• Total ratio parts: 7 + 3 = 10
• Milk quantity: (7/10) * 80 litres = 56 litres
• Water quantity: (3/10) * 80 litres = 24 litres

2. Desired Ratio:

• Desired milk to water ratio: 2 : 1

3. Water Addition:

• Let 'x' litres of water be added.
• New water quantity: 24 + x litres
• Milk quantity remains the same: 56 litres

4. Set Up Equation:

• We want the new ratio to be 2 : 1.
• So, 56 / (24 + x) = 2 / 1

5. Solve for x:

• 56 = 2(24 + x)
• 56 = 48 + 2x
• 2x = 56 - 48
• 2x = 8
• x = 8 / 2
• x = 4

Therefore, 4 litres of water should be added.

The correct answer is Option 4.