In what ratio should water be mixed with milk so that on selling the mixture at cost price a profit of 20% is made?

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

The core principle is that profit is earned by selling the added water (assumed to be free) at the cost price of the milk.
The formula for this scenario is: Profit % = (Quantity of Water / Quantity of Milk) × 100.
Substituting the given profit of 20%, we get: 20 = (Water / Milk) × 100.
Solving for the ratio gives Water / Milk = 20 / 100 = 1/5. Therefore, the required ratio of water to milk is 1:5.

Option B: This ratio represents the ratio of water to the total mixture (1 part water + 5 parts milk = 6 parts mixture). The question asks for the ratio of water to milk.
Option C: A ratio of 1:4 (water to milk) would result in a profit of 25%, calculated as (1/4) × 100. The desired profit is 20%.
Option D: A ratio of 1:3 (water to milk) would result in a profit of approximately 33.33%, calculated as (1/3) × 100. This is not the desired profit.

Visual 1: No visual is required for this type of quantitative aptitude question.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Profit and Loss in Mixtures as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude, a common component in the non-nursing sections of competitive nursing entrance exams.
Strong analytical and mathematical skills are essential for interpreting data, calculating medication dosages, and managing resources in a clinical setting.
What if the profit desired was 25%? The ratio of water to milk would need to be 1:4, as (1/4) × 100 = 25%.

How to Approach the Question

Identify the core of the problem: the mixture is sold at the cost price of the main component (milk), and profit comes from the added component (water), which is assumed to be free.
Recognize that the profit percentage is calculated on the cost of the milk, not the total volume of the mixture.
Use the direct formula: Profit % = (Quantity of cheaper substance / Quantity of dearer substance) × 100.
Plug in the given profit percentage: 20 = (Water / Milk) × 100.
Solve the equation to find the ratio of Water to Milk: Water/Milk = 20/100 = 1/5.
Select the option that matches the calculated ratio of 1:5.

Concept Tested & Keywords

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