if 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

Let's denote the first number as xxx and the second number as yyy. According to the problem:

45 of x=23 of y\frac{4}{5}\text{ of }x=\frac{2}{3}\text{ of }y54​ of x=32​ of y

This can be written as:

45x=23y\frac{4}{5}x=\frac{2}{3}y54​x=32​y

To find the ratio xy\frac{x}{y}yx​, solve for xxx in terms of yyy:

45x=23y\frac{4}{5}x=\frac{2}{3}y54​x=32​y

Multiply both sides by 54\frac{5}{4}45​:

x=23y×54=2×53×4y=1012y=56yx=\frac{2}{3}y\times \frac{5}{4}=\frac{2\times 5}{3\times 4}y=\frac{10}{12}y=\frac{5}{6}yx=32​y×45​=3×42×5​y=1210​y=65​y

Therefore,

xy=56\frac{x}{y}=\frac{5}{6}yx​=65​

Final answer:

The ratio of the first number to the second number is 5:6\boxed{5:6}5:6​.