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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Question : If the income of R is 30% more than the income of Q and the income of Q is 20% more than the income of P, the income of R is how much percentage more than the income of P?
Option 1: 56%
Option 2: 28%
Option 3: 44%
Option 4: 51%
Question : The smallest among the numbers $2^{250},3^{150},5^{100}$, and $4^{200}$ is:
Option 1: $4^{200}$
Option 2: $5^{100}$
Option 3: $3^{150}$
Option 4: $2^{250}$
Question : The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are:
Option 1: 2, 3 and 5
Option 2: 10, 15 and 25
Option 3: 8, 12 and 20
Option 4: 4, 6 and 10
Question : The fourth proportion of numbers 8, 20 and 15 is:
Option 1: 37.5
Option 2: 10
Option 3: 10.6
Option 4: 200
Question : Two numbers are 10% and 25% less than a third number. By what percentage must the second number be increased to make it equal to the first number?
Option 1: 16.67%
Option 2: 20%
Option 3: 15%
Option 4: 60%
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