Question

Apart 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. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs.1180 as hostel charges. Find the fixed charges and the cost of food per day​

Answer 1

$\huge\underline{\underline{\texttt{{Question:}}}}$

• Apart 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. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs.1180 as hostel charges. Find the fixed charges and the cost of food per day

$\huge\underline{\underline{\texttt{{Given:}}}}$

• student A takes food for 20 days she has to pay Rs. 1000
• student B takes food for 26 days, pays Rs.1180

$\huge\underline{\underline{\texttt{{To\:Find:}}}}$

• Fixed Charges and the cost of food per day = ?

$\huge\underline{\underline{\texttt{{Solution:}}}}$

Let the fixed charge Be Rs. x and the variable charge be Rs. y per day

It is given that when a Student A takes food for 20 days she has to pay Rs. 1000, as hostel charges,

$\huge\underline{\underline{\texttt{{Therefore:}}}}$

$\bold{x + 20y = 1000}$

$\implies{x = 1000 - 20y} \: \: ...(1)$

It is also given that When a Student B takes food for 26 days she had to pay Rs. 1180, as hostel charges.

$\huge\underline{\underline{\texttt{{Therefore\:We\:have:-:}}}}$

$\bold{x - 26y = 1180}$

Let us now substitute the value of x from equation 1 as follows :

$\bold{x - 26y = 1180}$

$\implies{ - 20y + 26y = 1180 - 1000}$

$\implies{6y = 180}$

$\implies{y = \frac{180}{6} }$

$\implies{y = 30}$

Now, substitute the value of y in equation 1 :

$\bold{x = 1000 - (20 \times 30) = 1000 - 600 = 400}$

Therefore x = 400 and y = 30.

$\huge\underline{\underline{\texttt{{Hence:}}}}$

$\star{\boxed{\sf{The \: fixed \: charge \: is \: Rs.400}}}$

$\star{\boxed{\sf{The \: variable \: charge \: is \: Rs.30 \: per \: day}}}$

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