Question

12. 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 1000 as hostel charges whereas a student B, who takes
food for 26 days, pays 1180 as hostel charges. Find the fixed charges and cost of
food per day. What habit grows in a child by staying in hostel?
1​

Answer 1

AnSwer:

• Let the fixed charge be Rs. x

• Let the variable charge be Rs. y per day.

★ According to the question,

Student A takes food for 20 days she has to pay Rs. 1000 as hostel charges, therefore,

So, the equation obtained is,

$⇢ \: \sf \: x+20y=1000 \\ \\ ⇢ \: \sf \: x=1000 - 20y.....(1)$

Similarly,

Student B takes food for 12 days she has to pay Rs. 1180 as hostel charges, therefore,

Equation obtained is,

$⇢ \sf \: x+26y=1180$

★ Now, according to the substitution method,

$⇢ \sf \: \: \: x+26y=1180 \\ \\ \sf⇢ \: \: 1000 - 20y+26y=1180 \\ \\⇢ \: \: \sf - 20y+26y=1180 - 1000 \\ \\ ⇢ \sf \: \: 6y=180 \\ \\ ⇢ \sf \: \: \: y = \dfrac{180}{6} \\ \\ ⇢ \sf \: \: \: y = 30$

Now put the value of y in eqn (1),

$⇢ \sf \: \: \: x = 1000 - (20 \times 30) \\ \\ ⇢ \sf \: \: \: x = 1000 - 600 \\ \\ ⇢ \sf \: \: \: x = 400$

Therefore , the fixed charges is Rs. 400 and the variable charges is Rs. 30 per day.