Question

Three times one number is equal to five times the other. If the sum of two numbers is 80, find the numbers.

• A. $25$ and $55$
• B. $50$ and $30$
• C. $45$ and $35$
• D. $60$ and $20$

Answer 1

Answer: (B)

$50$ and $30$

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

It is given that three times one number is equal to five times the other that is:

$3x=5y$

$3x-5y=\mathrm{0..........}\left(1\right)$

Also, the sum of the numbers is $80$ that is:

$x+y=\mathrm{80..........}\left(2\right)$.

Multiply the equation 2 by $3$:

$3x+3y=\mathrm{240..........}\left(3\right)$

Now subtract equation 1 from equation 3 to eliminate $x$, because the coefficients of $x$ are same. So, we get

$(3x-3x)+(3y+5y)=240-0$

i.e. $8y=240$

i.e. $y=30$

Substituting this value of $y$ in (1), we get

$3x-150=0$

i.e. $3x=150$

i.e. $x=50$

Hence, the two numbers are $50$ and $30$.