Question

Divide 80 into two numbers, such that 5 times one number is equal to 3 times the other number.

• A. $30and50$
• B. $35and52$
• C. $40and60$
• D. $22and49$

Answer 1

The correct option is A $30and50$

Let the two numbers be $x$ and $y$
Given,
$x+y=80$ (i) and
$5x=3y$
$⟹x=\frac{3y}{5}$ (ii)
Putting the value of $x$ in equation (i) we get,
$x+y=80$
$⟹\frac{3y}{5}+y=80$
$⟹\frac{3y+5y}{5}=80$
$⟹8y=400$
$⟹y=50$
Putting the value of $y$ in equation (i) we get,
$x+y=80$
$⟹x+50=80$
$⟹x=80-50$
$⟹x=30$
$\therefore x=30,y=50$