The probability that it will rain on Monday is 0.3. The probability that Ramya brings an umbrella on monday is 0.6.

What is the probability that Ramya does not bring an umbrella, given that it rains on Monday?

The question uses the Bayes theorem., but it can also be solved by thinking logically 

Essentially, we are given that it rains, and when it rains, Ramya brings the umbrella with a probability of 0.6. Hence the probability that she does not bring the umbrella on Monday is 0.4

These are two independent events and hence do not affect each other. 
The question states that is rains; the probability of Ramy not having an umbrella is independent of this and can directly be answered to be 0.4

Using Bayes theorem too, we get the same answer:$$\frac{0.4\times\ 0.6}{0.4\times\ 0.6\ +\ 0.6\times\ 0.6}=0.4$$

Hence, Option A is the correct answer.