If `4/3` of `P=2/3` of Q, then what is `P:Q` ?

Options

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

Answer

To solve the problem, we start with the equation given in the question:

\[ \frac{4}{3} P = \frac{2}{3} Q \]

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the equation by 3. This gives us:

\[ 3 \cdot \frac{4}{3} P = 3 \cdot \frac{2}{3} Q \]

This simplifies to:

\[ 4P = 2Q \]

### Step 2: Rearranging the equation
Next, we can rearrange the equation to express \(P\) in terms of \(Q\):

\[ 4P = 2Q \implies P = \frac{2Q}{4} \]

This simplifies to:

\[ P = \frac{Q}{2} \]

### Step 3: Finding the ratio \(P:Q\)
Now we can express the ratio \(P:Q\):

\[ P:Q = \frac{Q}{2}:Q \]

To express this in a simpler form, we can divide both parts of the ratio by \(Q\):

\[ P:Q = \frac{1}{2}:1 \]

This can be rewritten as:

\[ P:Q = 1:2 \]

### Final Answer
Thus, the ratio \(P:Q\) is:

\[ \boxed{1:2} \]

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