If in the fraction $x / y$ we decrease the numerator $x$ by $40 \%$ and the denominator $y$ by $60 \%$, then the fraction $x / y$
(a)decreases by $20 \%$;
(b)increases by $20 \%$;
(c)decreases by 50\%;
(d)increases by $50 \%$.
The correct option is (d).

If a number $x$ is decreased by $40\%$, it becomes $60\%$ of $x$, or $0.6 x$. Similarly, when a number $y$ is decreased by $60\%$, it becomes $0.4 y$. Therefore, the fraction $x / y$ becomes

$$
\frac{0.6 x}{0.4 y}=\frac{6}{4} \frac{x}{y}=1.5 \times \frac{x}{y}
$$

which means that the fraction $x / y$ has increased by $50\%$ of its value.