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In a city there were 600 restaurants which make at least one the three Updated on: 15 Jul 2019, 23:57
Originally posted by CareerGeek on 14 Jul 2019, 07:39.
Last edited by CareerGeek on 15 Jul 2019, 23:57, edited 1 time in total.
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C
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65% (hard)

Question Stats:

71% (03:11) correct 29% (03:12) wrong based on 274 sessions

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In a city there were 600 restaurants which make at least one the three food items out of Chinese, Continental and South Indian. The number of restaurants who make only Continental were 4 times of those who make only South Indian. The number of restaurants who make only Continental and Chinese were 1/5 of those who make only Chinese. The number of restaurants who make only Chinese were 3/4 times of those who make only continental. If 220 restaurants make South Indian, how many make Continental and Chinese only?

A. 10
B. 20
C. 30
D. 35
E. 73
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C
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In a city there were 600 restaurants which make at least one the three 16 Jul 2019, 02:38
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Dillesh4096
In a city there were 600 restaurants which make at least one the three food items out of Chinese, Continental and South Indian. The number of restaurants who make only Continental were 4 times of those who make only South Indian. The number of restaurants who make only Continental and Chinese were 1/5 of those who make only Chinese. The number of restaurants who make only Chinese were 3/4 times of those who make only continental. If 220 restaurants make South Indian, how many make Continental and Chinese only?

A. 10
B. 20
C. 30
D. 35
E. 73
Show more


Please see attached image for solution

IMO C
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In a city there were 600 restaurants which make at least one the three 15 Jul 2019, 23:53
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This is a poorly worded question. A little difficult to comprehend.

number of restaurants who make only Continental and Chinese were 15 of those who make only Chinese?
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In a city there were 600 restaurants which make at least one the three 15 Jul 2019, 23:58
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RJ7X0DefiningMyX
This is a poorly worded question. A little difficult to comprehend.

number of restaurants who make only Continental and Chinese were 15 of those who make only Chinese?
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Hi,

Apologies for the error.
Corrected now.

Regards

Posted from my mobile device
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In a city there were 600 restaurants which make at least one the three 16 Jul 2019, 00:46
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No. of restaurants that do not make South Indian = (Only Chinese)+(Only Continental)+(Only Chinese and Continental) = 600-220 = 380

If the number of restaurants that make only South Indian is \(x\),

Only Continental = \(4x\)
Only Continental and Chinese = \(\frac{3}{5}x\)
Only Chinese = \(3x\)


\(4x+\frac{3}{5}x+3x=380\)

\(38x=1900\)

\(x=50\)

Only Continental and Chinese = \(\frac{3}{5}x = \frac{3}{5}*50 = 30\)

Answer is (C)
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In a city there were 600 restaurants which make at least one the three 16 Jul 2019, 14:23
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Dillesh4096
In a city there were 600 restaurants which make at least one the three food items out of Chinese, Continental and South Indian. The number of restaurants who make only Continental were 4 times of those who make only South Indian. The number of restaurants who make only Continental and Chinese were 1/5 of those who make only Chinese. The number of restaurants who make only Chinese were 3/4 times of those who make only continental. If 220 restaurants make South Indian, how many make Continental and Chinese only?

A. 10
B. 20
C. 30
D. 35
E. 73
Show more

So I did make a Venn diagram of three variables and found 4x, 3/5x, 3x and only x. I could have solved it but I checked options. The only option that is divisible by 3 is 30. So marked C :) It doesn't make a whole lot of difference but still.
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In a city there were 600 restaurants which make at least one the three 11 Oct 2020, 06:06
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Dillesh4096
In a city there were 600 restaurants which make at least one the three food items out of Chinese, Continental and South Indian. The number of restaurants who make only Continental were 4 times of those who make only South Indian. The number of restaurants who make only Continental and Chinese were 1/5 of those who make only Chinese. The number of restaurants who make only Chinese were 3/4 times of those who make only continental. If 220 restaurants make South Indian, how many make Continental and Chinese only?

A. 10
B. 20
C. 30
D. 35
E. 73
Show more
Solution:

Since there are 600 restaurants in total and 220 restaurants make South Indian, 600 - 220 = 380 restaurants make Chinese or Continental. So:

380 = Only Chinese + Only Continental + Only Chinese and Continental

Let x = the number of restaurants that make only Chinese and Continental. Since the number of restaurants who make only Continental and Chinese are 1/5 of those who make only Chinese, the number of restaurants that make only Chinese is 5x. Further, we are told that the number of restaurants who make only Chinese were 3/4 times of those who make only continental; thus:

Only Chinese = 3/4 * Only continental

5x = 3/4 * Only continental

Only continental = 5x / (3/4) = 5x * 4/3 = 20x/3

Now, we can calculate the value of x:

380 = Only Chinese + Only Continental + Only Chinese and Continental

380 = 5x + 20x/3 + x

380 = 15x/3 + 20x/3 + 3x/3 = 38x/3

x = 380 * 3/38 = 30

So, there are x = 30 restaurants that make only Chinese and Continental.

Answer: C

Note: We did not have to use the fact that “The number of restaurants who make only Continental were 4 times of those who make only South Indian.”
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In a city there were 600 restaurants which make at least one the three 18 Dec 2025, 09:06
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