Question

Question 18
Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5, then find the numbers.

Answer 1

Let the two numbers be x and y
Then, by first condition, ratio of these two numbers = 5 : 6
x:y = 5: 6
$\frac{x}{y}=\frac{5}{6}\Rightarrow y=\frac{6x}{5}$
And by second condition, then, 8 is subtracted from each of the numbers, then ratio becomes 4:5
$\frac{x-8}{y-8}=\frac{4}{5}\Rightarrow 5x-40=4y-32\Rightarrow 5x-4y=8$
Now, put the value of y in Eq. (ii), we get
$5x-4\left(\frac{6x}{5}\right)=8\Rightarrow 25x-24x=40\Rightarrow x=40$
Put the value of x in Eq (i), we get
$Y=\frac{6}{5}\times 40=6\times 8=48$
Hence, the required numbers are 40 and 48