Question

Two numbers are in the ratio $7:5$ and their difference is $20$. What is the smaller number?

• A. $50$
• B. $70$
• C. $30$
• D. $68$

Answer 1

Answer: (A)

$50$

Let $x$ and $y$ be the two numbers. Then
$\frac{x}{y}=\frac{7}{5}$ and $x-y=20$
Cross multiplying the proportion
$5x=7y$ or $y=\frac{5}{7}x$
So, $x-y=20$
$x-\frac{5}{7}x=20\Rightarrow \frac{7x-5x}{7}=\frac{2x}{7}=20$
$\Rightarrow x=\frac{140}{2}=70$
$y=\frac{5}{7}x=\frac{5}{7}\times 70=50$
So smaller number is 50.
Check $:\frac{x}{y}=\frac{70}{50}=\frac{7}{5}and70-50=20$