Q) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days, she has to pay Rs. 1,500 as hostel charges while another student B, who takes food for 26 days, pays Rs. 1,800. Find the fixed charges and the cost of food.

Ans:

Step 1: Let’s consider the fixed charge is X and variable charge per day is Y

By 1st given condition, student A takes food for 20 days, she has to pay Rs. 1,500 as hostel charges

∴ X + 20 Y = 1500 ….. (i)

Step 2: By 2nd given condition, student B, takes food for 26 days and pays Rs. 1,800

∴ X + 26 Y = 1800 …. (ii)

Step 3: By subtracting equation (i) from equation (ii), we get:

(X + 26 Y ) – (X + 20 Y) = 1800 – 1500

∴ 6 Y = 300

∴ Y =

∴ Y = 50

Step 4: By substituting value of Y in equation (i), we get:

X + 20 Y = 1500

∴ X + 20 x 50 = 1500

∴ X + 1000 = 1500

∴ X = 1500 – 1000

∴ X = 500

Therefore, the fixed charges are Rs. 500 and the cost of food is Rs. 50.

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