Question

The ratio of three numbers is 3:4:5 and the sum of their squares is 1250. The sum of the numbers is-
$$\begin{gathered} A\text{ 30} \\ \text{B 50} \\ \text{C 60} \\ \text{D 90} \end{gathered}$$

Answer 1

Hint- Here we will proceed by assuming the required numbers be 3x, 4x and 5x. Then we will add the square of assumed numbers with the given value such that we will get the sum of numbers.

Complete step-by-step answer:

Let the numbers be 3x, 4x, 5x.
Also we are given that the sum of squares of those three numbers is 1250.
$\Rightarrow 9x^2+16x^2+25x^2=1250$
$\Rightarrow 50x^2=1250$
$\Rightarrow x^2={\displaystyle \frac{1250}{50}}$
$$\begin{gathered} \Rightarrow x^2=25 \\ \Rightarrow x=\sqrt{25} \\ \Rightarrow x=5 \end{gathered}$$
Sum of numbers = 3x + 4x + 5x = 12x
Now we will substitute the value of x = 5 in the sum of numbers i.e. 12x.
$\Rightarrow 12\times 5={60}^{}$
Therefore, the sum of those three numbers is 60.

Note- In this question we can assume any variable instead of x. Also one must be very clear about the fundamental mathematics as this question was totally based on it.