Question 14 Marks
A hotel has 320 rooms and 32 cleaners to maintain them. With full capacity of staff, it took 2 h to clean all the rooms.
(i) On Monday 20% of the cleaners were not available. Will the cleaning of all rooms takes more time? How can you say so?
(ii) Ishan says, "The number of cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms."
Mira says, "The number of clearners available in the hotel is inversely proportional to the time taken by them to clean the rooms."
Who is correct? Given reason.
(iii) Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?
(iv) The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?
(a) The total number of room increases by 2
(b) The total number of room decreases by 2
(c) The total number of room increases by 3
(d) The total number of room decreases by 3
(i) On Monday 20% of the cleaners were not available. Will the cleaning of all rooms takes more time? How can you say so?
(ii) Ishan says, "The number of cleaners available in the hotel is directly proportional to the time taken by them to clean the rooms."
Mira says, "The number of clearners available in the hotel is inversely proportional to the time taken by them to clean the rooms."
Who is correct? Given reason.
(iii) Equal number of rooms are allocated for each staff member for cleaning. How many rooms each cleaner had to maintain?
(iv) The hotel administration hired 8 more cleaners. What is the change in number of rooms maintained by each cleaner?
(a) The total number of room increases by 2
(b) The total number of room decreases by 2
(c) The total number of room increases by 3
(d) The total number of room decreases by 3
Answer
View full question & answer→(i) Yes, because with $20 \%$ less staff, work has to be performed by available staff impacting the total time.
(ii) Mira is correct.
Because the more number of staff available in the hotel for cleaning, less time will be required to finish it which means the number of room cleaning staff available in the hotel is inversely porportional to the time taken by them to clean the rooms.
(iii) Since, to clean 320 rooms, the required cleaners are 32.
$\therefore$ Number of rooms each cleaners had to maintain
$
=\frac{320}{32}=10 rooms
$
(iv) (b) The hotel administration hired 8 more cleaners.
$\therefore$ Number of cleaners $=32+8=40$
and number of rooms $=320$
$\therefore$ Each cleaner will maintain the number of rooms
$
=\frac{320}{40}=8
$
Previously, they had to maintain 10 rooms.
$\therefore$ Change in number of rooms maintained by each cleaner $=10-8=2$
(ii) Mira is correct.
Because the more number of staff available in the hotel for cleaning, less time will be required to finish it which means the number of room cleaning staff available in the hotel is inversely porportional to the time taken by them to clean the rooms.
(iii) Since, to clean 320 rooms, the required cleaners are 32.
$\therefore$ Number of rooms each cleaners had to maintain
$
=\frac{320}{32}=10 rooms
$
(iv) (b) The hotel administration hired 8 more cleaners.
$\therefore$ Number of cleaners $=32+8=40$
and number of rooms $=320$
$\therefore$ Each cleaner will maintain the number of rooms
$
=\frac{320}{40}=8
$
Previously, they had to maintain 10 rooms.
$\therefore$ Change in number of rooms maintained by each cleaner $=10-8=2$