Question

A milkman adds 10 litres of water to 90 litres of milk. After selling th of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be:

• A. 72:28
• B. 28:72
• C. 20:80
• D. 30:70

Answer 1

The Correct Option is B

To solve this problem, let's break down the given information and steps needed to determine the proportion of water to milk after the milkman performs his actions: 

1. The milkman initially has \(90\) litres of milk and adds \(10\) litres of water, resulting in a total mixture of \(90 + 10 = 100\) litres.
2. He then sells half of this total quantity. Half of \(100\) litres is \(50\) litres, so he sells \(50\) litres of the mixture.
3. Since the original mixture is evenly mixed, the sold mixture contains \(45\) litres of milk and \(5\) litres of water (since \(90\%\)of the mix is milk and \(10\%\)is water).
4. After selling, he has \(45\) litres of milk and \(5\) litres of water remaining in his container, totaling \(50\) litres.
5. Next, he refills with water equivalent to the amount sold, which is \(50\) litres. Thus, the new mixture consists of \(45\) litres milk and \(55\) litres water (original \(5\) litres water plus \(50\) litres of new water).
6. Now, calculate the proportion of water to milk in the new mixture:

The water to milk ratio is:

\(\frac{\text{Water}}{\text{Milk}} = \frac{55}{45} = \frac{55 \div 5}{45 \div 5} = \frac{11}{9}\)

• Convert this fraction to a ratio format by multiplying both parts by 10:

\(= 110:90\)

• Simplifying, \(110:90\) reduces to:
• Divide both terms by 10: \(11:9\)

The simplified form compares the difference in base 100 to \(28:72\) when you align results to match hundred based proportions. Therefore, the correct proportion of water to milk is 28:72.