A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?  Choose the correct choice from the following choices.
A) 67/90  B) 29/60  C) 17/30  D) 19/30  E) 11/15
I think A - 67/90 is the correct answer.   Here goes:   Lets assume originally the number of beds = x   After the new tower, the total combined no of beds = 7x   So old = x, New = 6x   Now 1/3 of x are occupied and 1/5 of 6x are occupied which simplifies to (6/5)x   We are shifting 1/3 of x to the new ward so there will now be:   1/3 of x plus 6/5 of x occupied in the new ward. Add them up to get 23/15 of x   There are 6x beds in New Tower so ratio is:   (23/15)x / 6x = 23/90 of x   Subtract that from 90/90 of x and you get the number of un-occupied beds to total capacity of New Tower = 67/90.   67/90
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A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?