The ratio of the first number to the second number is 5 : 3.

Quick Step-by-step Explanation

Let:

  • First number = AAA
  • Second number = BBB

Given:

  • 40% of the first number = two-third of the second number
  • Mathematically: 40%\\text{of}\A=\dfrac{2}{3}\\text{of}\B

So:

40%\text{ of }A=\dfrac{40}{100}A=\dfrac{2}{3}B

\dfrac{2}{5}A=\dfrac{2}{3}B

Cancel 2 from both sides:

\dfrac{1}{5}A=\dfrac{1}{3}B

Now:

\frac{A}{B}=\frac{5}{3}

So, the ratio of the first number to the second number:

A:B=5:3

Answer: \boxed{5:3}

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