Question

the ratio of two positive numbers (X and Y) is 3:5. when 2 is added to both the numbers the ratio of X to Y becomes 5:8 . what is the difference between both the numbers.

Answer 1

hello users ......

we have given that ..

The ratio of two positive numbers (X and Y) is 3:5 
and 
  when 2 is added to both the numbers the ratio of X to Y becomes 5:8

we have to find the difference between both numbers =? 

according to question 
  x : y = 3 : 5
=.> x/y = 3/5
=> 5x = 3y
 => 5x - 3y =0
=> 40x - 24y = 0 ...........(1)   (multiply both by 8 )
and 
 (x+2) : (y+2) = 5 : 8
=> (x+2)/(y+2) = 5/8  
=> 8 (x+2)  = 5(y+2) 
= 8x - 5y = 10 - 16 
=> 8x -5y = -6  or 8x - 5y +6 = 0
=> 40x - 25y +30 = 0.......(2)      ( multiply both by 5)

now subtracting (1) from  (2).....
.....
we get 
-25y +30 + 24y = 0
=> -y +30 = 0 
=> y = 30 

now putting the value of y in (1) we get 
40x - 24 (30) = 0
=> 40x - 720 = 0 
=> 40x = 720 
=> x = 18 

now the difference between these numbers 
= 30 - 18 = 12 answer 

hence 
the two numbers are 30 and 18 
and there difference is 12 answer

☆☆ hope it helps ☆☆