If 30% of P = 40% of Q. then g is how much percent less than P2

Options

A. 20
B. 25
C. 12.5
D. 10

Answer

To solve the problem step by step, we start with the given equation and work towards finding how much percent less G is than P.

### Step 1: Set up the equation from the given information
We know that:
\[ 30\% \text{ of } P = 40\% \text{ of } Q \]

This can be written mathematically as:
\[ 0.3P = 0.4Q \]

### Step 2: Rearranging the equation to find a relationship between P and Q
To express Q in terms of P, we can rearrange the equation:
\[ Q = \frac{0.3P}{0.4} \]
\[ Q = \frac{3P}{4} \]

### Step 3: Find G in terms of P
We need to determine how G relates to P. Let's assume G is some percentage of P. We can express G as:
\[ G = kP \]
where k is the percentage (in decimal form) we need to find.

### Step 4: Find the value of G
Since we don't have a specific value for G given in the problem, we can assume that G is equal to Q for the sake of this problem. Thus:
\[ G = Q = \frac{3P}{4} \]

### Step 5: Calculate how much percent G is less than P
To find how much percent G is less than P, we can use the formula:
\[ \text{Percentage less} = \left( \frac{P - G}{P} \right) \times 100\% \]
Substituting G with \(\frac{3P}{4}\):
\[ \text{Percentage less} = \left( \frac{P - \frac{3P}{4}}{P} \right) \times 100\% \]

### Step 6: Simplify the expression
Calculating the numerator:
\[ P - \frac{3P}{4} = \frac{4P}{4} - \frac{3P}{4} = \frac{P}{4} \]

Now substituting back into the percentage formula:
\[ \text{Percentage less} = \left( \frac{\frac{P}{4}}{P} \right) \times 100\% \]
\[ = \left( \frac{1}{4} \right) \times 100\% = 25\% \]

### Conclusion
Thus, G is 25% less than P.

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