If 15% of x is equal to three times 10% of y, then what is the ratio x : y?

Introduction / Context:This is a basic percentage and ratio problem that checks the ability to translate verbal percentage relationships into algebraic equations. Once we write the relationship between 15% of x and 10% of y, the ratio x : y can be easily found by simple algebraic manipulation. Such questions are very common in quantitative aptitude tests.

Given Data / Assumptions:

• 15% of x is equal to three times 10% of y.
• We must find the simplified ratio x : y.
• Both x and y are assumed to be positive real numbers.

Concept / Approach:We will write the given statement as an equation using percentage to decimal conversion. Then we isolate the ratio x/y. Finally, we simplify the fraction obtained to get the ratio in simplest whole number form. Understanding that percent just means “per hundred” is enough for this question.

Step-by-Step Solution:

Verification / Alternative check:Choose a simple value to test the ratio. Let y = 1, so x = 2. Then 15% of x = 15% of 2 = 0.30. Ten percent of y = 0.10. Three times 10% of y = 3 * 0.10 = 0.30. Both sides are equal, confirming that the relationship is satisfied when x : y = 2 : 1.

Why Other Options Are Wrong:

• 1 : 2 would imply x is smaller than y, which contradicts x = 2y.
• 3 : 2 and 2 : 3 do not satisfy the equation 0.15x = 0.30y when substituted.

Common Pitfalls:Common mistakes include mixing up which value is multiplied by 3 or misreading “three times 10% of y” as “30% of y” without proper algebra. While 3 * 10% does equal 30%, it is important to clearly write it as 3 * 0.10y before simplifying. Another error is to forget to simplify the ratio fully, but here 2 : 1 is already in simplest form.

Final Answer:The required ratio is 2 : 1.