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  • Directions for question Mr N Chandrasekaran, Chairman of the Taj Group of Hotels, in the process of investigating the reason for the not so goo

Directions for question

Mr N Chandrasekaran, Chairman of the Taj Group of Hotels, in the process of investigating the reason for the not so good financial performance of the top ten hotels of their group in the financial year 2022-23, initiated two surveys.

The survey was to be done specifically for the following top ten hotels of their group : 1) Taj Palace (Delhi), 2) Taj Coromandel (Chennai), 3) Taj Bengal (Kolkata), 4) Taj Skyline (Ahmedabad), 5) Taj Chandigarh (Chandigarh), 6) Taj Malabar (Cochin), 7) Umaid Bhawan Palace (Jodhpur), 8) Taj Ganges (Varanasi), 9) Taj Chia Kutir (Darjeeling) and 10) Taj Exotica (Andaman).

In 2021-22, a certain number of people went to these hotels (collectively) and in 2022-23, these people again visited one or more of these 10 hotels. 

One of the surveys was to find out what percentage of the first time guests of these top ten hotels of their group repeated their visit at these ten hotels in the financial year 2022-23. The second was to find out what percentage of those who repeated their visit at these ten hotels in the financial year 2022-23, were there for business purposes. 

The following was the result of the survey in the form of a line graph with two components :

 

Question

It was known that in the Financial Year 2022-23, the guests who repeated their stay at the Umaid Bhawan Palace (Jodhpur), and the guests who repeated their stay at another hotel out of the remaining nine (say the hotel is Taj Z), did not repeat their stay at any other hotel. Assuming that none of the repeat guests of the Umaid Bhawan Palace (Jodhpur) repeated their stay at Taj Z, and vice versa, how many of the nine hotels, excluding the Umaid Bhawan Palace (Jodhpur), can be Taj Z ? 

 

 

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

We know that :

 

Name of Hotel

% of the first time guests who repeated their visit among the hotels, in the financial year 2022-23

% of those who were on a repeat visit for business purpose only, in the Financial year 2022-23

% of the first time guests who were on a repeat visit for business purpose only, in the Financial year 2022-23

1

Taj Palace (Delhi)

15%

75%

75% of 15% = (75*15)/100 = 11.25%

2

Taj Coromandel (Chennai)

10%

55%

55% of 10% = (55*10)/100 = 5.50%

3

Taj Bengal (Kolkata)

40%

55%

55% of 40% = (55*40)/100 = 22.00%

4

Taj Skyline (Ahmedabad)

30%

70%

70% of 30% = (70*30)/100 = 21.00%

5

Taj Chandigarh (Chandigarh)

30%

60%

60% of 30% = (60*30)/100 = 18.00%

6

Taj Malabar (Cochin)

15%

45%

45% of 15% = (45*10)/100 = 6.75%

7

Umaid Bhawan Palace (Jodhpur)

45%

25%

25% of 45% = (25*45)/100 = 11.25%

8

Taj Ganges (Varanasi)

20%

65%

65% of 20% = (65*20)/100 = 13.00%

9

Taj Chia Kutir (Darjeeling) 

25%

30%

30% of 25% = (30*25)/100 = 7.50%

10

Taj Exotica (Andaman)

10%

15%

15% of 10% = (15*10)/100 = 1.50%

 

45% (which is the highest percentage) of the first time guests of the top ten hotels of the Taj group, as listed above, repeated their visit at Umaid Bhawan Palace (Jodhpur) in the Financial Year 2022-23. These 45% repeat guests did not stay in any other hotel out of the remaining nine.

Let the percentage of first time guests of the top ten hotels of the Taj group, as listed above, who repeated their visit at Taj Z in the Financial Year 2022-23 be x%

In the Financial Year 2022-23, none of the guests of the top ten hotels who repeated their stay at the Umaid Bhawan Palace (Jodhpur) repeated their stay at Taj Z, and vice versa (as per condition). 

Hence, we can say that (45+x)% of the first time guests of the top ten hotels of the group repeated their visit at these two hotels in the Financial Year 2022-23.

The remaining, that is, 100 – (45+x) = (55 – x)% of the first time guests would have repeated their visit at the remaining eight hotels in the Financial Year 2022-23.

The second highest percentage of the first time guests of the top ten hotels of the Taj group, as listed above, who repeated their visit at any of the hotels is 40% (Taj Bengal, Kolkata).

Since we do not know which of the nine hotels, apart from Umaid Bhawan Palace (Jodhpur), Taj Z is, the value of (55 – x)% must be at least 40%. Hence the value of x can be at the most (55 – 40) = 15%

The value of the percentage of first time guests of the top ten hotels of the Taj group who repeated their visit at the hotels is at most 15% for Taj Coromandel (Chennai), Taj Exotica (Andaman), Taj Palace (Delhi) and Taj Malabar (Cochin), that is four hotels. 

Hence, Taj Z can be 4 of the nine hotels excluding the Umaid Bhawan Palace (Jodhpur)

 

 

Posted by

Anam Khan

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