I think D - 19/30 is the correct answer.
Lets assume originally the number of beds = x
After the new tower, the total combined no of beds = 3x
So old = x, New = 2x
Now 1/3 of x are occupied and 1/5 of 2x are occupied which simplifies to (2/5)x
We are shifting 1/3 of x to the new ward so there will now be:
1/3 of x plus 2/5 of x occupied in the new ward. Add them up to get 11/15 of x
There are 2x beds in New Tower so ratio is:
(11/15)x / 2x = 11/30 of x
Subtract that from 30/30 of x and you get the number of un-occupied beds to total capacity of New Tower.
Is D the correct answer?
"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde