We usually take the ratio as k:1, if it is not given to us,for the ease of solving the question.Because here we only need to find value of 1 variable , which is k.But if you take the ratio as something like x:y , it is difficult as you need to find out the value of 2 variables.So usually we take the ratio as k:1 and then solve for k to get the ratio.For eg: if the actual ratio is 2:3, and if we take the ratio as k:1, then we will get value of k as 2/3 after solving.Therefore the ratio is(2/3):1 which is equal to 2:3.
Don't worry read it carefully and do remember that you have to take the ratio as k:1 in these kinds of problems.