Verified answer

(3+x)/(5+x) = 1/2

2(3+x) = (5+x)

6 + 2x = 5 + x

x = –1

check

(3–1)/(5–1) = 2/4 = 1/2

( 3  + x ) / ( 5   + x )    = 1 / 2

6  + 2 x   = 5  + x

x   =   - 1

Number is (-1)

The number, which if added to both of terms of the ratio 3 : 5,

then it becomes 1 : 2

Let the numbers be   3  and  5 . When y is added to both,

we get  (3 + x)  : :  (5 + x)  : :  1 : 2  

If x = -1

(3 - 1)  : :  (5 - 1)  : :  2 : 4 or 1 : 2     

So the number is - 1.

Let the number be n. Then (3+n):(5+n) = 1:2. Put n = -1. Then (3-1):(5-1) = 2:4 = 1:2.

(3x + n) / (5x + n) = 1/2

2 * (3x + n) = 1 * (5x + n)

6x + 2n = 5x + n

6x - 5x = n - 2n

x = -n

-x = n

No matter what we start with, as long as n = -x, we'll get what you're looking for.  For instance, if we have 30/50, then x = 10

(30 - 10) / (50 - 10) = 20/40 = 1/2

600/1000

3x = 600

x = 200

n = -200

(600 - 200) / (1000 - 200) =>

400/800 =>

1/2

So if you have a number (3x)/(5x), then (3x - x) / (5x - x) = 2x/(4x) = 1/2

The number needed is -1 because (3-1)/(5-1) = 1/2