If increasing 20 by P percentage gives the same result as decreasing 60 by P percentage,what is P percentage of 70?

Options

A. 50
B. 140
C. 14
D. 35

Answer

To solve the problem step by step, let's break it down:

### Step 1: Set up the equation
We know that increasing 20 by P percentage gives the same result as decreasing 60 by P percentage. We can express this mathematically:

\[ 20 + \left(\frac{P}{100} \times 20\right) = 60 - \left(\frac{P}{100} \times 60\right) \]

### Step 2: Simplify the equation
Let's simplify both sides:

\[ 20 + \frac{20P}{100} = 60 - \frac{60P}{100} \]

This can be rewritten as:

\[ 20 + 0.2P = 60 - 0.6P \]

### Step 3: Combine like terms
Now, let's move all terms involving P to one side and constant terms to the other side:

\[ 0.2P + 0.6P = 60 - 20 \]

This simplifies to:

\[ 0.8P = 40 \]

### Step 4: Solve for P
Now, we can solve for P by dividing both sides by 0.8:

\[ P = \frac{40}{0.8} = 50 \]

### Step 5: Find P percentage of 70
Now that we have P, which is 50, we need to find 50% of 70:

\[ \frac{50}{100} \times 70 = 35 \]

### Final Answer
Thus, the answer is:

\[ \text{P percentage of 70 is } 35. \]

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