Question

A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days one has taken food in the mess. When a student a takes food for 20 days, he has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charge and the cost of food per day.

Answer 1

$\huge\mathbb{\underline{SOLUTION:-}}$

★ Now, A takes food for 20 days and pays Rs. 1000.

★ That is, 20x+y=1000 .................(1)

★ Also, B takes food for 26 days and pays Rs. 1180.

★ That is, 26x+y=1180 ..................(2)

Subtracting (1) from (2), we get,

• 6x=180

• i.e. x =30

Substitute x=30 in (1), we get,

• 20(30)+ y=1000

• i.e. 600 +y=1000

• i.e. y = 400

Hence, the fixed charges are Rs. 400 and the cost of food per day is Rs. 30.

_______________________________

Answer 2

Step-by-step explanation:

Let x be the fixed charge of the food and y be the charge for food

per day.

According to the given information,

x + 20y = 1000 (1)

x + 26y – 1180 (2)

Subtracting equation (1) from equation (2), we obtain

6y = 180

y = 30

Substituting this value in equation (1), we obtain

x + 20 × 30 = 1000

x = 1000 – 600

x = 400

Hence, fixed charge = Rs 400

And charge per day = Rs 30