Question : There are three numbers P, Q, and R. 30 percent of P is equal to the 15 percent of Q. 20 percent of Q is equal to the 10 percent of R. By what percent is R more than P?
Option 1: 150%
Option 2: 300%
Option 3: 200%
Option 4: 250%
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Correct Answer: 300%
Solution :
Given, 30% of P = 15% of Q ⇒ ($\frac{30}{100}$)P = ($\frac{15}{100}$)Q ⇒ P = ($\frac{1}{2}$)Q
also, 20% of Q = 10% of R ⇒ ($\frac{20}{100}$)Q = ($\frac{10}{100}$)R ⇒ Q = ($\frac{1}{2}$)R
from the above two relations, we get,
P = ($\frac{1}{4}$)R
⇒ R = 4P
$\therefore$ R is more than P by $\frac{\text{R}-\text{P}}{\text{P}}$ × 100 = $\frac{4\text{P}-\text{P}}{\text{P}}$ × 100 = 300%
Hence, the correct answer is 300%.
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