Question
The total expenses of a hostel are partly fixed and
partly variable with the number of boys, the change is Rs 200 per head when there are 50 boys and Rs 175 per head when there are 100 boys. Find the charge per head when there are 125 boys in the hostel?Solution
Let the total charge of hostel be Rs x and Variable charges is Rs y x + y/50 = 200 ……………….(i) x + y/100 = 175 ……………….(ii) By solving these equations, we get y/50 - y/100 = 25 y/100 = 25 y = Rs 2,500 Putting the value of y in eq (i), we get x + 2,500/50 = 200 x + 50 = 200 x = Rs 150 So charge per head when there are 125 boys in the hostel x + y/125 = 150 + 2,500/125 = 150 + 20 = Rs 170
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