Question

The sum of two numbers is 11 and their difference is 4. Then the two numbers

• A. $8\frac{1}{2}$ and $4\frac{1}{2}$.
• B. $7\frac{1}{2}$ and $3\frac{1}{2}$
• C. $6\frac{1}{2}$ and $2\frac{1}{2}$.
• D. $8\frac{1}{2}$ and $2\frac{1}{2}$.

Answer 1

The correct option is B

$7\frac{1}{2}$ and $3\frac{1}{2}$

Let the two numbers be $x$ and $y$.

Let us assume that $x$ is greater than $y$.

Given, the sum of these two numbers is 11. i.e. $x+y=11$

Also, given that, the difference of these two numbers is 4. i.e. $x-y=4$

We know that $(x+y)+(x-y)=2x$

Then, $11+4=2x$

$⟹2x=15$

$⟹x=7.5=7\frac{1}{2}$

Then $x+y=11$ implies that $y=3\frac{1}{2}$ [$x-y=4$ may be considered too]

Hence the two required numbers are $7\frac{1}{2}$ and $3\frac{1}{2}$.