Two numbers are respectively 20 percent and 50 percent more than a third number. These two numbers are in the ratio.

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let the third number be }}x \cr & {\text{Then,}} \cr & {\text{first number}} \cr & = 120\% {\text{ of }}x = \frac{{120}}{{100}}x = \frac{{6x}}{5} \cr & {\text{And, second number}} \cr & = 150\% {\text{ of }}x = \frac{{150}}{{100}}x = \frac{{3x}}{2} \cr & \therefore {\text{Required ratio}} \cr & = \frac{{6x}}{5}:\frac{{3x}}{2} \cr & = 12:15 \cr & = 4:5 \cr} $$