Each of the 150 residents of TG colony can be classified as having either a pet dog or pet cat, as vegetarian or as non-vegetarian, as living on first floor or ground floor.
It is further known that
1. The number of non-vegetarian residents is half the number of vegetarians.
2. The number of residents who live on ground floor is twice the number of residents who live on first floor.
3. The number of vegetarians having dog is same as the number of first floor residents having a pet dog.
4. The number of residents living on first floor having a non-vegetarian diet and pet cat, is one more than the number of residents living on ground floor who are vegetarian and have a pet dog.
5. The number of residents with a pet cat is 54 more than those with pet dog.

1) Find the difference between the number of residents living on ground floor who have non-vegetarian diet and pet cat, and the number of residents living on first floor who are vegetarian and have a pet dog.

a)2                                 b)1                            c)3                                 d)4

Sol. b)1
Let the table represent the various classified groups of residents.
From statement 1, we can conclude that a+b+c+d=50 (I)
& e+f+g+h = 100 (II)
From statement 2, we can conclude that b+d+f+h=50 (III)
& a+c+e+g = 100 (IV)
From statement 3, we can conclude that c+g=c+d or g=d (V)
From statement 4, we can conclude that b=g+1 (VI)
From statement 5, we can conclude that a+b+e+f=102 (VII)
& c+d+h+g = 48 (VIII)

Now, we need to calculate |c-f|.
Using III & V: 1+2d+f+h=50
Using V & Vii: c+2d+h = 48
Subtracting the equations, we get f-c = 1 (IX)