Two numbers are respectively 30 percent and 40 percent less than a third number. What percent of the first number is the second number ?

Given:

First number is 30% less than the third number.

Second number is 40% less than the third number.

Lets take the third number to be 100.

First number = $100 - 30$% of $100$

= $100 - \dfrac{30}{100} \times 100$

= $100 - \dfrac{30}{\cancel{100}} \times \cancel{100}$

= $100 - 30$

= $70$

Second number = $100 - 40$% of $100$

= $100 - \dfrac{40}{100} \times 100$

= $100 - \dfrac{40}{\cancel{100}} \times \cancel{100}$

= $100 - 40$

= $60$

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

= $\dfrac{60}{70} \times 100$ %

= $\dfrac{6}{7} \times 100$ %

= $\dfrac{600}{7}$ %

= $85\dfrac{5}{7}$ %

Hence, the percent of the first number is the second number = $85\dfrac{5}{7}$ %.