If two quantities x and y vary inversely with each other, then which one of the following is true?

Question

Accepted Answer

When two quantities, x and y, vary inversely with each other, it means that as one quantity increases, the other decreases in such a way that their product remains constant. This relationship can be mathematically expressed as:

$$ x \times y = k $$

where $ k $ is a constant.

**Explanation for Option 2: Product of their corresponding values remains constant.**

- In an inverse variation, the defining characteristic is that the product of the two variables is always equal to a constant value. This means that if you multiply the value of x by the value of y at any point, the result will always be the same constant $ k $. This is the fundamental property of inverse variation, making Option 2 the correct answer.

**Explanation for why the other options are incorrect:**

1. **Option 1: Ratio of their corresponding values remains constant.**
   - In inverse variation, the ratio of x to y does not remain constant. Instead, as one variable increases, the other decreases, which means their ratio changes. Therefore, this option is incorrect.

2. **Option 3: Summation of their corresponding values remains constant.**
   - The sum of x and y does not remain constant in inverse variation. The sum can vary widely depending on the specific values of x and y, as their relationship is defined by their product, not their sum. Hence, this option is incorrect.

3. **Option 4: Difference of their corresponding values remains constant.**
   - Similar to the summation, the difference between x and y is not constant in inverse variation. The difference can change as the values of x and y change, since their relationship is governed by their product. Thus, this option is also incorrect.

In conclusion, the defining feature of an inverse variation is that the product of the two quantities remains constant, which is why Option 2 is the correct answer.