Question

There are 1500 restaurants in a city. Among these restaurants, 520 of Chinese cuisine, 335 offer North Indian
cuisine, 425 offer South Indian cuisine, 100 offer both South indian and Chinese Cuisines, 180 offer both Chinese
and North Indian cuisines, 150 offer both North and South Indian cuisines and 28 ofer all the three cuisines.
How many Restaurants offer only Chinese cuisine?​

Answer 1

Answer : 728 restaurants in total offer chinese cuisine. But only 520 offer only chinese and nothing else

Step-by-step explanation:

Answer 2

Given: There are 1500 restaurants in a city. Among these restaurants, 520 of Chinese cuisine, 335 offer North Indian cuisine, 425 offer South Indian cuisine, 100 offer both South Indian and Chinese Cuisines, 180 offer both Chinese and North Indian cuisines, 150 offer both North and South Indian cuisines and 28 offer all the three cuisines.

To find: Restaurants that offer only Chinese cuisine

Explanation: Let n(A) be number of North Indian restaurants,n(B) be number of South Indian restaurants and n(C) be number of Chinese restaurants.

n(A)= 335

n(B)= 425

n(C)= 520

Now, total restaurants= (A∪B∪C) = 1500

Restaurants offering South Indian and Chinese= n(B∩C)= 100

Restaurants offering North Indian and Chinese=n(A∩C)= 180

Restaurants offering North Indian and South Indian=n(A∩B)= 150

Number of restaurants that offer all 3 = n(A∩B∩C)= 28

Restaurants offering only Chinese= Restaurants offering Chinese- Restaurants offering Chinese and North Indian- Restaurant offering Chinese and South Indian- Restaurants offering all three

Restaurants offering only Chinese=n(C)- n(A∩C)-n(B∩C)-n(A∩B∩C)

= 520-180-100-28

= 212

Therefore, 212 restaurants are offering only Chinese cuisine.