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 first condition we get 

x:y = 4:5 ,
x/y = 4/5
5 x  = 4 y                                  --- ( 1 )

And from second condition we get
(x-30) / (y-30) = 1/2
x − 30y − 30 = 1/2 ,

2 x  - 60 = y -  30 ,

2 x - y =  30                         --- ( 2 )

x= 40
y = 50

Answer 2

HI !

Let the no:s be 4x and 5x 

4x - 30 / 5x - 30 = 1/2

5x - 30 = 2(4x - 30)

5x - 30 = 8x - 60

8x - 5x = -30 + 60

3x = 30

x = 10

4x = 40
5x = 50

∴ The no:s are 40 and 50