Question

In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?

• A. 1 : 5
• B. 5 : 1
• C. 1 : 6
• D. 5 : 6

Hint:

When a mixture is sold at the cost price of the pure component and there is a gain, the gain percentage is directly related to the ratio of the cheaper (or free) component to the pure component. If the gain is \(x\)\%, then the ratio of the cheaper component to the pure component is \(x : 100\) or \(x/100 : 1\).

Answer 1

The Correct Option is A

Step 1: Understand the concept of gain at cost price.
If the mixture is sold at the cost price of pure milk and a gain of 20\% is achieved, it means that the 20\% gain is due to the addition of water. Step 2: Assume the quantity of pure milk.
Let the quantity of pure milk be 100 units (it can be liters, etc.). Step 3: Calculate the quantity of gain.
Gain = 20\% of the cost price of pure milk. Since the mixture is sold at the cost price of pure milk, the gain is effectively 20\% of the cost of the milk. This gain is due to the water added. Step 4: Relate the gain to the cost price of water.
Since water is usually considered to have no cost, the entire gain comes from selling the added water at the price of milk. Step 5: Determine the quantity of water.
A 20\% gain on 100 units of milk means that the value of the added water is equivalent to 20 units of milk. Since the mixture is sold at the cost price of milk, these 20 units of value must come from the water. Therefore, the quantity of water added is 20 units. Step 6: Find the ratio of water to milk.
Ratio of water to milk = Quantity of water : Quantity of milk = 20 : 100 Step 7: Simplify the ratio.
Divide both parts of the ratio by their greatest common divisor, which is 20. Ratio = \( \frac{20}{20} : \frac{100}{20} = 1 : 5 \)