Which of the following statement (s) is ? Are ture?
(A) Ratio has no units
(B) a :b is the same as b:a

Options

A. only A
B. only B
C. A and B
D. Neither A nor B

Answer

To determine which of the given statements is true, let's analyze each one step by step.

### Step 1: Analyze Statement (A)
**Statement (A): Ratio has no units.**

- A ratio compares two quantities of the same kind. For example, if we compare the number of apples to the number of oranges, we can express this as a ratio.
- When we write a ratio, we are essentially dividing two quantities that have the same unit. For instance, if we say there are 3 apples and 6 oranges, we can express the ratio of apples to oranges as 3:6.
- Since both quantities are in terms of count (unitless), when we form a ratio, the units cancel out.
- Therefore, the statement "Ratio has no units" is **true**.

### Step 2: Analyze Statement (B)
**Statement (B): a : b is the same as b : a.**

- This statement suggests that the ratio of a to b is equal to the ratio of b to a.
- To understand this, let's use an example. If we take a = 1 and b = 2, then:
- The ratio a : b = 1 : 2.
- The ratio b : a = 2 : 1.
- Clearly, 1 : 2 is not the same as 2 : 1. They represent different relationships between the quantities.
- Thus, the statement "a : b is the same as b : a" is **false**.

### Conclusion
- Statement (A) is true: **Ratio has no units.**
- Statement (B) is false: **a : b is not the same as b : a.**

### Final Answer
- The true statement is (A) only.

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