Question : If 50% of (P – Q) = 30% of (P + Q) and Q = $x$% of P, then the value of $x$ is:
Option 1: 30
Option 2: 25
Option 3: 20
Option 4: 50
Correct Answer: 25
Solution :
Given: 50% of (P – Q) = 30% of (P + Q)
⇒ 50 × (P – Q) = 30 × (P + Q)
⇒ 50P – 50Q = 30P + 30Q
⇒ 20P = 80Q
⇒ $\frac{\text{P}}{\text{Q}}$ = $\frac{80}{20}$ = $\frac{4}{1}$
⇒ Q = $\frac{P}{4}$
According to the question,
Q = $x$% of P
⇒ $\frac{P}{4}=\frac{x}{100}\times $ P
⇒ $x=\frac{100}{4}=25$
Hence, the correct answer is 25.
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