UGC NET Questions (Paper – 1)

A proportion is an equation that states that two ratios are equal, such as a:b = c:d. It indicates that the relative relationship between the first pair of quantities is the same as that between the second pair. In mathematical aptitude, many word problems use proportions to relate parts and wholes or to scale quantities. Therefore, equality of two ratios is correctly described by the term proportion.

Option A:
Variation refers to how one quantity changes in relation to another, such as direct or inverse variation, but it is not specifically about equality of two numerical ratios. While variation also deals with relationships, it does not necessarily state that two ratios are equal. Hence, this term does not match the precise condition mentioned in the question.

Option B:
Proportion is correct because it captures the idea "two ratios are equal" in a single term. For instance, if 2:3 = 4:6, we say 2, 3, 4 and 6 are in proportion. This concept is widely used in problems involving scale diagrams, recipes and map reading. Thus, option B aligns perfectly with the wording of the question.

Option C:
Inverse usually refers to inverse proportion or inverse relationship where one quantity increases while the other decreases, maintaining a constant product. It does not refer to an equality of two ratios directly. Therefore, it is not an accurate response to the specific description in the stem.

Option D:
Percentage is a way of expressing a ratio out of 100, but it is not the term used solely for equality of two ratios. You can express each ratio as a percentage, yet the fact that percentages match does not change the underlying terminology: the equality is still called a proportion. Thus, this option is not the best answer.

This option is correct because when two ratios are equal, we say they are in proportion. The notation a:b = c:d indicates that a/b equals c/d. Such an equality is called a proportion in standard arithmetic terminology. Therefore, the situation described in the question defines a proportion.

Option A:
Variation describes how one quantity changes when another changes, such as direct or inverse variation. It does not specifically refer to the equality of two ratios. Hence, variation is not the term used for a:b = c:d.

Option B:
A proportion is an equation that states two ratios are equal. In the example a:b = c:d, the four terms are said to be in proportion. This matches exactly the relationship described by the question, so proportion is the correct name.

Option C:
Commission is a fee or percentage earned on sales or transactions. It belongs to commercial arithmetic rather than ratio equality. Since the question is about two ratios being equal, commission is irrelevant.

Option D:
Percentage is a way to express a number per hundred, such as 30%. Although percentages are related to ratios, the specific term used when two ratios are equal is proportion, not percentage. Therefore, this option is not correct.