Question

In a student hostel one third of total no of girls and four more only take vegetarian food,one fourth and three more take non veg only. the other 103 take both veg and nan veg food. how many girls are there in hostel

Answer 1

Take 'x' to be the total no. of girls.

Then veg. only girls would be ⅓ of x plus 4 = ⅓x + 4
Non-veg. only girls = ¼x + 3
Both veg and non veg = 103
Total = x

So, (x/3 + 4) + (x/4 + 3) + 103 = x

(4x+3x)/12 + 110 = x (LCM of 3 & 4)
7x/12 +110 = x
7x/12 + x = -110 (Transposing x and 110)
(7x-12x)/12 = -110 (LCM of the denominators)
-5x/12 = -110
-5x = -110 * 12 (Transposing 1/12)
-5x = -1320
x = -1320/-5 (Transposing -5)
x = 264


Therefore, the total number of girls in the hostel is 264

I hope you found my answer useful.

Answer 2

Answer:

So, (x/3 + 4) + (x/4 + 3) + 103 = x

(4x+3x)/12 + 110 = x (LCM of 3 & 4)

7x/12 +110 = x

7x/12 + x = -110  

(7x-12x)/12 = -110

-5x/12 = -110

-5x = -110 * 12  

-5x = -1320

x = -1320/-5

x = 264

Therefore, the total number of girls in the hostel is 264

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