Question

A 75-liter mixture contains milk and water in the ratio 3:2. If 15 liters of this mixture are removed and replaced with 10 liters of pure milk, what is the new ratio of milk to water in the mixture?

• A. 11:7
• B. 23:12
• C. 17:11
• D. 19:12

Answer 1

Answer:

B. 23:12

Initial mixture = 75 liters

Milk : Water = (3:2)

So,

$\text{Milk} = \frac{3}{5}\times 75 = 45 \text{ L}$
$\text{Water} = \frac{2}{5}\times 75 = 30 \text{ L}$

Remove 15 liters of mixture

Since the mixture ratio is (3:2):

Milk removed:

$\frac{3}{5}\times 15 = 9 \text{ L}$

Water removed:

$\frac{2}{5}\times 15 = 6 \text{ L}$

Remaining quantities:

$\text{Milk} = 45 - 9 = 36 \text{ L}$
$\text{Water} = 30 - 6 = 24 \text{ L}$

Total left:

$36 + 24 = 60 \text{ L}$

Add 10 liters of pure milk

New milk quantity:

$36 + 10 = 46 \text{ L}$

Water remains:

$24 \text{ L}$

New ratio of milk to water

$46:24$

Divide by 2:

$23:12$

Final Answer

The new ratio of milk to water is:

$\boxed{23:12}$