Question

Find two numbers, which differ by $7$, such that twice the greater added to five times the smaller gives $42$.

• A. $19$ and $12$
• B. $12$ and $5$
• C. $11$ and $4$
• D. $16$ and $9$

Answer 1

The correct option is C $11$ and $4$

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

It is given that two numbers differ by $7$

$\Rightarrow x-y=7$ $...\left(1\right)$

Also, twice the greater number added to five times the smaller gives $42$

$\Rightarrow 2x+5y=42$ $...\left(2\right)$

Multiply equation $\left(1\right)$ by $2$

$2x-2y=14$ $...\left(3\right)$

Let us subtract equation $\left(3\right)$ from equation $\left(2\right)$ to eliminate $x$, because the coefficients of $x$ are the same.

$(2x+5y)-(2x-2y)=42-14$

$\Rightarrow (2x-2x)+(5y+2y)=28$

$\Rightarrow 7y=28$

$\Rightarrow y=4$

Substituting this value of $y$ in $\left(1\right),$

we get $x-4=7$

i.e. $x=11$

Hence, the two numbers are $11$ and $4$