An item, when sold at a certain price, yields r% profit. Had it been s

Let "S" represents the Selling Price
Let "C" represents the Cost Price

Hence Initial profit (r%) = [(S-C)/C]*100 --------eq.(1)

Now they say if the Selling Price was $s more, the profit percentage would have been t%
Now lets try to evaluate this as below:
Hence New profit (t%) = [{(S+s) - C}/C]*100
Now let's try to breakdown the above equation
=> (t%) = {[(S-C)/C]*100} + {(s/C)*100}
Now if we look closely at the above breakdown the first part i.e. {[(S-C)/C]*100} is nothing but (r%) i.e. eq(1)
Hence the final Equation comes down to (Note: I am dropping % sign for more clarity in below equation):
=> t = r + [(s/c)*100]
=> (t - r) = (s/c) * 100
=> c = 100s/(t - r)

Which is nothing but Option (B)

Kudos are appreciated if you liked my solution.