Question

Two no. Are in the ratio 5:6 If 8 is subtracted from each the ratio become4:5find the number

Answer 1

let the original nos.be 5x and 4x
A/Q-
(5x-8) / (6x-8)=4÷5
25x-40=24x-32
25x-24x=40-32
x=8
therefore,5x=40
6x=48

Answer 2

Let the two numbers be x and y.

Then by first condition,ratio of these two numbers is 5:6.

         x:y = 5:6

         x/y = 5/6

           y = 6x/5        ........(1)

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

            x-8/y-8 = 4/5

            5x-40 =4y-32

            5x-4y = 8       ..........(2)

Now put the value of y in eq(2),we get,

     5x-4(6x/5) = 8

     25x-24x = 40

                x = 40

Put the value of x in eq(2),we get,

    y = 6/5 × 40

       = 48

The required numbers are 40 and 48.