In a students' hostel, one third of the total number of girls and four more take vegetarian food only, one fourth and three more take non-vegetarian food only. The other 103 take both vegetarian and non-vegetarian food. How many girls are there in the hostel?

Let the total number of girls be x.
No. of girls who take vegetarian food only = x + 4
No. of girls who take non - vegetarian food only = x + 3
No. of girls who take both vegetarian and non - vegetarian food = 103.By the given condition,
x + 4 + x + 3 + 103 = x
x + x - x + 110 = 0 Multiply through out by 12,
4x + 3x - 12x + 1320 = 0
-5x + 1320 = 0
-5x = -1320
x =
x = 264∴ There are 264 girls in the hostel.