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

Given:

First number is 20% of the third number.

Second number is 50% of the third number.

Lets take the third number to be 100.

First number = $20$% of $100$

= $\dfrac{20}{100} \times 100$

= $\dfrac{20}{\cancel{100}} \times \cancel{100}$

= $20$

Second number = $50$% of $100$

= $\dfrac{50}{100} \times 100$

= $\dfrac{50}{\cancel{100}} \times \cancel{100}$

= $50$

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

= $\dfrac{50}{20} \times 100$ %

= $\dfrac{5}{2} \times 100$ %

= $\dfrac{500}{2}$ %

= $250$%

Hence, the percent of the first number is the second number = 250 %.