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The expenditure on food of a guesthouse is partly fixed and partly variable, varying with the number of guests. If there are 20 guests, then each of the guests has to bear Rs. 650 per month and if there are 5 more guests, then the share of each of the guests comes down by Rs. 50 per month. How many guests were there, if the share of each guest is Rs. 500?

The expenditure on food of a guesthouse is partly fixed and partly variable, varying with the number of guests. If there are 20 guests, then each of the guests has to bear Rs. 650 per month and if there are 5 more guests, then the share of each of the guests comes down by Rs. 50 per month. How many guests were there, if the share of each guest is Rs. 500? Correct Answer 50

Let the fixed expense be x and the variable expense be y per head.

x + 20y = 20 × 650 = 13000    ----(1)

And, x + 25y = 25 × 600 = 15000     ----(2)

From equations (1) and (2)

⇒ x = 5000

⇒ y = 400

Let, the required number of students be n.

⇒ 5000 + n × 400 = n × 500

⇒ n = 50

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