60% of P = 50% of Q and Q=x% of P. What is the value of x?

Options

A. 130
B. 120
C. 140
D. 80

Answer

To solve the problem step by step, we start with the given equations:

1. **Equation Setup**:
We have two equations from the problem statement:
- \( 60\% \text{ of } P = 50\% \text{ of } Q \)
- \( Q = x\% \text{ of } P \)

2. **Convert Percentages to Fractions**:
We can express the percentages as fractions:
- \( 60\% \text{ of } P = \frac{60}{100} \times P = 0.6P \)
- \( 50\% \text{ of } Q = \frac{50}{100} \times Q = 0.5Q \)

So, we can rewrite the first equation as:
\[ 0.6P = 0.5Q \]

3. **Rearranging the First Equation**:
To eliminate the decimals, we can multiply both sides by 10:
\[ 6P = 5Q \]

4. **Expressing Q in Terms of P**:
Now, we can express \( Q \) in terms of \( P \):
\[ Q = \frac{6}{5}P \]

5. **Substituting Q in the Second Equation**:
Now we substitute \( Q \) in the second equation \( Q = x\% \text{ of } P \):
\[ \frac{6}{5}P = \frac{x}{100}P \]

6. **Canceling P from Both Sides**:
Since \( P \) is common on both sides and not equal to zero, we can cancel it out:
\[ \frac{6}{5} = \frac{x}{100} \]

7. **Cross Multiplying**:
To solve for \( x \), we cross-multiply:
\[ 6 \times 100 = 5 \times x \]
\[ 600 = 5x \]

8. **Solving for x**:
Now, divide both sides by 5:
\[ x = \frac{600}{5} = 120 \]

Thus, the value of \( x \) is **120**.