Question

$\frac{p}{q}$ and $\frac{x}{y}$ are two rational numbers, such that 'q' and 'y' are positive, and
if $p\times y$ < $q\times x$, then ________.

• A. $\frac{p}{q}$ < $\frac{x}{y}$
• B. $\frac{p}{q}$ > $\frac{x}{y}$
• C. $\frac{p}{q}$ = $\frac{x}{y}$
• D. None of the above

Answer 1

The correct option is A $\frac{p}{q}$ < $\frac{x}{y}$

Given: $\frac{p}{q}$ and $\frac{x}{y}$ are rational numbers.
If we take any two rational numbers, such that 'q' and 'y' are positive, for example,
$\frac{1}{4}$ and $\frac{3}{5}$

Given: $p\times y$ < $q\times x$ = $1\times 5$ < $4\times 3$ = 5 < 12
Making the denominators of $\frac{1}{4}$ and $\frac{3}{5}$ equal, we get,
$\frac{1}{4}$ = $\frac{5}{20}$ and

$\frac{3}{5}$ = $\frac{12}{20}$

Now, $\frac{5}{20}<\frac{12}{20}$
$\therefore$ $\frac{p}{q}<\frac{x}{y}$