Question

The ratio of three numbers is $3:4:5$ and the sum of their squares is $1250$. The sum of the three numbers is:

• A. $60$
• B. $90$
• C. $30$
• D. $50$

Answer 1

Answer: (A)

$60$

Let the three numbers be $3x,4x$ and $5x$.
Given $(3x{)}^2+(4x{)}^2+(5x{)}^2=1250$
$9x^2+16x^2+25x^2=1250$
$\Rightarrow 50x^2=1250\Rightarrow x^2=25\Rightarrow x=5$
$\therefore$ The three numbers are $3\times 5,4\times 5$ and $5\times 5$ i.e., $15,20$ and $25$
Required sum $=15+20+25=60$