In a survey of 215 people a pet food manufacturer found that

In a survey of 215 people, a pet food manufacturer found that 53 owned a dog but not a cat, 23 owned a cat but not a dog, and 82 owned neither a dog or a cat. How many owned both a cat and a dog? How many owned a dog?

Solution

Total no of person found in survey 215

Persson having only Dog = 53

Persson having only Cat = 23

Person {neither dog nor cat } = 82

so

(a) Persson having Dog and Cat both = Total - [only Dog + only Cat +Person {neither dog nor cat }]

   = 215 - [53+23+82]

= 57

(b) Person owned Dog = Persson having only Dog + Persson having Dog and Cat both{bcoz atleast having adog}

   = 53 + 57

   = 110

Answer