If a number is reduced by 40% it becomes two-thirds of another number. What is the ratio of the first number to the second number ?

Let the numbers be $$x$$ and $$y$$ respectively
Then,
60% of $$x$$ = $$\frac{{2}}{{3}}$$ $$y$$
⇒ $$\frac{{60}}{{100}}$$ $$x$$ = $$\frac{{2}}{{3}}$$ $$y$$
⇒ $$\frac{{3}}{{5}}$$ $$x$$ = $$\frac{{2}}{{3}}$$ $$y$$
⇒ $$\frac{{x}}{{y}}$$ = $$\frac{{2}}{{3}}$$ × $$\frac{{5}}{{3}}$$
⇒ $$\frac{{x}}{{y}}$$ = $$\frac{{10}}{{9}}$$
∴ x : y = 10 : 9