Total 190 people attended a marriage ceremony in which 122 people ate palak paneer, 93 people ate dosa and 75 people ate biryani, if 37 people ate both biryani and palak paneer, 38 people ate both dosa and biryani, 45 people ate both dosa and palak paneer and 20 people ate all the three dishes. How many persons ate only one dish?

Total 190 people attended a marriage ceremony in which 122 people ate palak paneer, 93 people ate dosa and 75 people ate biryani, if 37 people ate both biryani and palak paneer, 38 people ate both dosa and biryani, 45 people ate both dosa and palak paneer and 20 people ate all the three dishes. How many persons ate only one dish? Correct Answer 110

Number of persons who ate palak paneer n(P) = 122

Number of persons who ate dosa n(D) = 93

Number of persons who ate biryani n(B) = 75

Number of persons who ate both biryani and palak paneer n(B ⋂ P) = 37

Number of persons who ate both biryani and dosa n(B ⋂ D) = 38

Number of persons who ate both palak paneer and dosa n(P ⋂ D) = 45

Number of persons who ate all the three dishes n(B ⋂ D ⋂ P) = 20

∴ Number of people who ate only palak paneer = n(P) – n(P ⋂ D) – n(B ⋂ P) + n(B ⋂ D ⋂ P) = 122 – 37 – 45 + 20 = 60

Number of people who ate only dosa = n(D) – n(P ⋂ D) – n(B ⋂ D) + n(B ⋂ D ⋂ P) = 93 – 38 – 45 + 20 = 30  

Number of people who ate only biryani = n(B) – n(B ⋂ P) – n(B ⋂ D) + n(B ⋂ D ⋂ P) = 75 – 37 – 38 + 20 = 20

∴ Persons who ate only one dish = 60 + 30 + 20 = 110  

 Additional Information

People having Only Palak paneer : 60