Question

Two numbers are in the ratio 4 : 5. If 30 is subtracted from each of the numbers, the ratio becomes 1 : 2. Find the numbers.

Answer 1

Let given two numbers are ' x ' and 'y',

So from the first condition, we get

$x:y=4:5,\frac{x}{y}=\frac{4}{5}5x=4y5x-4y=0---\left(1\right)$

And from the second condition we get

$\frac{x-30}{y-30}=\frac{1}{2}2x-60=y-30,2x-y=30---\left(2\right)$

$\left(2\right)\times 48x-4y=120---\left(3\right)\left(3\right)-\left(1\right)8x-4y-(5x-4y)=120-08x-4y-5x+4y=1203x=120x=40$

Put value of x in (2)

$y=2x-30=2\times 40-30=80-30=50x=40y=50$