Question

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

So y = 6x/5

and by second condition, then, 8 is subtracted from each of the numbers, then ratio becomes 4:5

(x-8)/(y-8) = 4/5

5(x-8) = 4(y-8)

5x – 4y = 8

Now, put the value of y in Eq. (ii), we get

5x – 4 ( 6x/5 ) = 8

So x/5 = 8

And x = 40

Put the value of x in Eq. (i), we get

So, y = (6/5 x 40) = 48

Hence, the required numbers are 40 and 48.