If the price of milk is $ 15\%$ more than that of water, then the price of water is approximately what percent

Question

If the price of milk is $ 15\%$ more than that of water, then the price of water is approximately what percentage less than that of milk?

Examoogle · Accepted Answer

The correct answer is Option D: 13.04%. Use the formula $$\frac{r}{100+r} 	imes 100$$ where $r$ is the percentage increase. For $r = 15$, this is $$\frac{15}{115} 	imes 100 = \frac{3}{23} 	imes 100 \approx 13.04\%$$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the formula $$\frac{r}{100+r} 	imes 100$$ where $r$ is the percentage increase. For $r = 15$, this is $$\frac{15}{115} 	imes 100 = \frac{3}{23} 	imes 100 \approx 13.04\%$$.

Formula Used: $$Percentage = \left( \frac{x}{100 + x} ight) 	imes 100$$

Given: Price of milk is 15% more than the price of water.

Steps: Define the base price: Assume the price of water is 100 units.. Calculate the price of milk: Since milk is 15% more than water, add 15% of 100 to the base price.. Calculate the percentage difference: To find how much less water is than milk, find the difference relative to the price of milk.

Answer: D is correct because the price of water relative to the price of milk is $$(15 / 115) 	imes 100$$, which equals approximately 13.04%.

Exam Tip: This concept is fundamental in Profit & Loss (e.g., mark-up vs discount percentage) and Speed-Time-Distance problems involving speed variations.

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