Question

The sum of two numbers is 405 and their ratio is 8 : 7. Find the numbers.

Answer 1

Let the first number = x

and the second number = y

According to the question,

x + y = 405 .....(i)

and the numbers are in the ratio 8 : 7

$i.e.\frac{8x}{7y}=1\Rightarrow 8x=7y\Rightarrow x=\frac{7}{8}y...\left(ii\right)$

Now, substitute the value of x in equation (i)

$\frac{7}{8}y+y=4057y+8y=405\times 815y=3240y=\frac{3240}{15}y=216$

Now, put the value of y in equation (ii)

$x=\frac{7}{8}\times 216x=189$

$\therefore$ Hence, the numbers are 189 and 216