Ratio and Proportion - Class 10 MCQ

The ratio of the original quantity (30) to the new quantity (45) is 30:45, which simplifies to 2:3 when both numbers are divided by their H.C.F. of 15. Ratios like this are often used to understand increases or decreases in quantities.

The compound ratio of 2:3 and 4:5 is calculated by multiplying the antecedents and the consequents. Thus, it is (2*4):(3*5) = 8:15. This concept is useful in various applications, including scaling recipes or other proportional adjustments.

The mean proportional is found by taking the square root of the product of the two numbers. So, √(4 * 16) = √64 = 8. Mean proportionals are often used in geometry and design to create balanced and aesthetically pleasing proportions.

The ratio 9:27 simplifies to 1:3 when both terms are divided by their H.C.F. of 9. In contrast, the other options can still be simplified further. Knowing how to reduce ratios is crucial for accurate comparisons in mathematics.

Let the fourth proportional be x. Setting up the ratio 2:3 = 4.5:x, cross-multiplying gives 2x = 3 * 4.5, leading to x = 6. This illustrates how proportions can help find unknown values in mathematical problems.

Incommensurable refers to quantities whose ratios cannot be expressed as a ratio of two integers. This concept is significant in advanced mathematics, particularly in understanding irrational numbers and their properties.

The ratio of 4 to 20 can be simplified by dividing both terms by their highest common factor (H.C.F.), which is 4. Thus, 4:20 simplifies to 1:5. Ratios express a relationship between quantities and are often used in real-world applications like finance and cooking.

To find the combined ratio a:b:c, we need a common term for b. Since a:b is 2:5 and b:c is 3:4, we can express b as 15 in both ratios. This gives us a = 6, b = 15, and c = 20, resulting in the combined ratio 6:15:20. This method of combining ratios is commonly used in solving problems involving multiple proportional relationships.

The correct relationship is a/b = c/d, indicating that the ratios are equivalent. This property is foundational in understanding proportions and can be utilized in solving problems that involve direct and inverse relationships.

In a ratio expressed as a:b, 'a' is referred to as the antecedent and 'b' as the consequent. Therefore, in the ratio 3:7, 3 is the antecedent. Understanding the terms of a ratio helps clarify relationships in various mathematical contexts.