Question

If the sum of two numbers is $84$ and their difference is $30$, the numbers are:

• A. $-57$ and $27$
• B. $57$ and $27$
• C. $57$ and $-27$
• D. $-57$ and $-27$

Answer 1

The correct option is B $57$ and $27$

Given, sum of two numbers is $84$.

Let the smaller number be $x$.

Then, larger number will be $84-x$.

Given, their difference is $30$.

Therefore, $84-x-x=30$

$\Rightarrow 84-2x=30$

$\Rightarrow 84-30=2x$

$\Rightarrow 54=2x$

$\Rightarrow x=27$

Smaller number is $27$.

Now, larger number is $84-x=84-27=57$.