Two numbers are respectively 20 percent and 50 percent more than a third number. What percent of the first number is the second number?

Given:

First number is 20% more than the third number.

Second number is 50% more than the third number.

Lets take the third number to be 100.

First number = $100 + 20$% of $100$

= $100 + \Big(\dfrac{20}{100} \times 100\Big)$

= $100 + \Big(\dfrac{20}{\cancel{100}} \times \cancel{100}\Big)$

= $100 + 20$

= $120$

Second number = $100 + 50$% of $100$

= $100 + \Big(\dfrac{50}{100} \times 100\Big)$

= $100 + \Big(\dfrac{50}{\cancel{100}} \times \cancel{100}\Big)$

= $100 + 50$

= $150$

Percentage of first number is to second number = $\dfrac{\text{Second number}}{\text{First number}} \times 100$ %

= $\dfrac{150}{120} \times 100$ %

= $\dfrac{5}{4} \times 100$ %

= $\dfrac{500}{4}$ %

= $125$%

Hence, first number is 125% of the second number.