Question

# If the ratio of two numbers is 3:5 and their sum is 360, then the numbers are 135 and 225If true then enter 1 and if false enter 0

Hint: We can assign a variable to the two numbers and form equations to find these variables.
First we will assume the two numbers to be x and y.

Now we will proceed with the question sequentially and form equations so we can find x and y.
The ratio of two numbers is 3:5 $\Rightarrow$ $x:y=3:5$
Now we know that ratios can also be written as divisions. Therefore, we can write
$\dfrac{x}{y}=\dfrac{3}{5}$
Multiplying both sides with $\dfrac{5}{3}$ we have
$\dfrac{5}{3}.\dfrac{x}{y}=\dfrac{5}{3}.\dfrac{3}{5}$
On simplification we get,
$\dfrac{5x}{3y}=1$
$\Rightarrow 5x=3y$
Therefore, we can write
$x=\dfrac{3}{5}y$ (i)
Now we have one equation. We need one more to find x and y.
The second statement of the question says,
The sum is 360 $\Rightarrow$ $x+y=360$ (ii)
After substituting the value of x from equation (i) in equation (ii) we have,
$\dfrac{3}{5}y+y=360$
Taking 5 as LCM we have,
$\dfrac{3y+5y}{5}=360$
$\Rightarrow \dfrac{8y}{5}=360$
Multiplying both sides with 5 we have,
$8y=360\times 5$
Multiplying both sides with 8 we have,
$y=\dfrac{360\times 5}{8}$
On calculating y we have,
$y=225$
Now that we have calculated y we can also calculate x from equation (ii)
$x+y=360$
$\Rightarrow x=360-y$
On substituting value of y we have,
$\Rightarrow x=360-225$
$\Rightarrow x=135$
Therefore, the numbers are 225 and 135.
Note: The only source of error here can be misreading the question and writing the wrong equations. One more thing to keep in mind is that we can write $x:y=\dfrac{x}{y}$ but we cannot write $x:y:z=\dfrac{\dfrac{x}{y}}{z}$ . It only applies when there are only two terms.