A is `(1)/(3)` less than B.
Find Ratio of `A:B=?`

Options

A. A) 1:1
B. B) 2:3
C. C) 3:2
D. D) 1:2

Answer

To solve the problem where A is \( \frac{1}{3} \) less than B, we can follow these steps:

### Step 1: Define B
Let's assume B is represented by a variable. We can let:
\[ B = 3x \]
where \( x \) is a positive number.

### Step 2: Calculate A
Since A is \( \frac{1}{3} \) less than B, we can express A as:
\[ A = B - \frac{1}{3}B \]
This simplifies to:
\[ A = B - \frac{1}{3}B = \frac{3}{3}B - \frac{1}{3}B = \frac{2}{3}B \]

Substituting \( B = 3x \) into the equation for A gives:
\[ A = \frac{2}{3}(3x) = 2x \]

### Step 3: Find the Ratio A:B
Now we can find the ratio of A to B:
\[ A:B = 2x:3x \]

### Step 4: Simplify the Ratio
To simplify the ratio, we can divide both terms by \( x \):
\[ A:B = 2:3 \]

### Final Answer
Thus, the ratio of A to B is:
\[ A:B = 2:3 \]

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