I think D - 19/30 is the correct answer.

Here goes:

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?

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