Instructions

Read the following passage:

On a picnic trip of a company, 3 hotels Trident, Hilton and Park were booked for 90 employees. 6 of theemployees were willing to stay at any hotel. 12 wanted to stay in only Trident. 18 wanted to stay in onlyPark. Only Hilton had two times the employees as there were in Trident and Park only. Only Hilton and Parkhad three less than only Trident and Hilton. Also not more than 7 employees can stay in only Trident andHilton.

Question 87

How many employees can stay in Hilton?

Solution

Now it is given that the total employees are 90, where $$Y+3\le7\ $$ or $$Y\le4$$

So, $$39+3X+2Y\ =\ 90$$

$$3X+2Y\ =\ 51$$

$$X=\ \frac{\left(51-2Y\right)}{3}$$

Now, since $$Y\le4$$, Y can only be 3.

Thus, X will be 15.

Now, total employees in Hilton = $$2X+2Y+9=36+9=45$$

Thus, the correct option is C.

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How many employees can stay in Hilton?

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