A certain hotel has 1,400 single rooms and 420 double rooms. Each room

Question

A certain hotel has 1,400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?

(A) 65
(B) 70
(C) 80
(D) 90
(E) 265

(A) 65 
(B) 70 
(C) 80 
(D) 90 
(E) 265

Skywalker18 · Accepted Answer

Number of single rooms= 1400
Number of double rooms = 420
Time taken by a person to clean a single room = 15 mins = 1/4 hour
Time taken by a person to clean a double room = 20 mins =1/3 hour

Total time to clean 1400 single and 420 double rooms
= 1400*1/4 + 420 * 1/3
= 350 + 140
= 490 hours

Each person works for = 7 hours

Number of persons required = 490/7 = 70

Answer B

rohit8865 · Answer

for single room, one person can clean 4 rooms in 1 hr.
thus in 7 hrs =7*4=28 rooms
Persons required for 1400 rooms= 1400/28= 50 persons
similarly
for double room, one person can clean 3 rooms in 1 hr.
thus in 7 hrs =7*3=21 rooms
Persons required for 420 rooms= 420/21 =20 persons

thus total no. of persons = persons required for single room + persons required for double rooms
=50 + 20=70

Ans B

generis · Answer

cleanersRTW.png 1) Use a modified RT = W formula. Add (# of workers) to LHS: (# of workers) * rate * time = Work Manipulate it just as you would RT = W 2) change cleaning rates from minutes to hours (All units must be the same. Each cleaner works 7 hours.) Single room cleaning rate in hours: \frac{1room}{15mins}=\frac{4rooms}{60mins}=\frac{4rooms}{1hour}= 4 Double room cleaning rate in hours: \frac{1room}{20mins}=\frac{3rooms}{60mins}=\frac{3rooms}{1hour}= 3 3) Calculate number of persons needed for each kind of room Single rooms \frac{W}{r*t}= number of cleaning persons needed \frac{1,400}{(4*7)}=\frac{1,400}{28}= 50 persons needed Double rooms \frac{W}{r*t}= number of cleaning persons needed \frac{420}{(3*7)}=\frac{420}{21}= 20 persons needed Total persons needed: (50 + 20) = 70 Answer B

EMPOWERgmatRichC · Answer

Hi All,

This is essentially a rate question. Here's how to solve it:

Single rooms take one person 15 minutes to clean and double rooms take one person 20 minutes to clean.

15 mins. = 1/4 hour 
20 mins. = 1/3 hour

With 1400 single rooms x 1/4 hour = 350 hours of total work for 1 person 
With 420 double rooms x 1/3 hour = 140 hours of total work for 1 person

For ALL the rooms, we have a total of 350 + 140 = 490 hours of total work for 1 person

To get the work done in 7 hours, we'll need 490/7 = 70 workers

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

BrentGMATPrepNow · Answer

The hotel has 1,400 single rooms, and one person can clean a single room every 15 minutes   
So, one person can clean 4 single rooms in ONE HOUR
In other words, it takes 1 WORKER HOUR to clean 4 single rooms

1400/4 = 350
So, it takes  350  WORKER HOURS to clean 1400 rooms

The hotel has 420 double rooms, and one person can clean a double room every 20 minutes   
So, one person can clean 3 double rooms in ONE HOUR
In other words, it takes 1 WORKER HOUR to clean 3 double rooms

420/3 = 140
So, it takes  140  WORKER HOURS to clean 420 double rooms

How many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?  
 350  +  140  =  490 
So,  490  WORKER HOURS are required to clean ALL of the room.

490 /7 = 70. 
So, 70 workers are needed.

Answer: B

Cheers, 
Brent

ScottTargetTestPrep · Answer

It takes 1400 x 1/4 = 350 hours to clean the single rooms and 420 x 1/3 = 140 hours to clean the double rooms, for a total time of 490 hours. We can let n = the number of workers and create the equation:

7n = 490

n = 70

Answer: B

AnirudhaS · Answer

total time to clean single rooms = 1400 * 15 = 21000 min
total time to clean double rooms = 420 * 20 = 8400 min
total time to clean both single & double rooms = 29400 min = 490 hours

1 worker works for = 7 hours
So, no. of workers = 490/7 = 70 workers

Answer:  B

100mitra · Answer

total time to clean single rooms = (1400 * 15 = 21000 min) / 60 mins = 350 hrs.
total time to clean double rooms = (420 * 20 = 8400 min) / 60 mins = 140 hrs 
manpower rate : (1/350) + (1/140) = (1/10)
manpower = 10 
task to complete in 7 hrs = 10 * 7 = 70 Manpower  option B

bumpbot · Answer

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A certain hotel has 1,400 single rooms and 420 double rooms. Each room

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