Three numbers are in the ratio 1 : 2 : 3. By adding 5 to each of them, the new numbers are in the ratio 2 : 3 : 4. The numbers are:

Initial ratio of the numbers 1:2:3

So, let the numbers be y , 2y , 3y

Now adding 5 to each number will give us y+5, 2y+5, 3y+5

as it is given that new ratio is 2:3:4 so assume that the new numbers are 2z, 3z, 4z

and hence we can relate numbers in following way:

y+5 = 2z............(1)

2y + 5 = 3z........(2)

3y+5 = 4z ...........(3)

from equation 1 and 2

y = 5 and z = 5

So initially the numbers are

(5 , 10 , 15 )