Question

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 cost of food per day.. 1180 as hostel charges. Find the fixed charges and the cost of food per day (BY CROSS MULTIPLICATION...)​

Answer 1

${\pmb{\underline{\sf{ Required \ Solution ... }}}}$

• Monthly hostel charges is fixed and the remaining depends on the number of days.

Let the Fixed charges be x and cost of food per day be y.

★As We know that:

• A takes food for 20 days For ₹1000
• B takes food for 26 days for ₹1180

★Equation be like:

• x + 20y = 1000
• x + 26y = 1180

$\begin{gathered} \boxed{\begin{array}{c} \\ \bigstar{\pmb{\underline{\sf{Elimination}}}} \\ \\ \sf{ -x-20y = -1000 } \\ \sf{x+26y = 1180} \\ {\underline{\sf{ \ \ \ 6y \ \ \ = \ \ \ \ \ \ 180 }}} \end{array}} \end{gathered}$

After Calculating, we've

$\colon\implies{\sf{ 6y = 180 }} \\ \\ \colon\implies{\sf{ y = \cancel{ \dfrac{180}{6} } }} \\ \\ \colon\implies{\sf{ y = 30_{(Cost \ Per \ Day)} }}$

»» By Putting values of one Variable in any Equation to get value of other variable as.

$\colon\implies{\sf{ x + 20y = 1000 }} \\ \\ \colon\implies{\sf{ x + 20 \times 30 = 1000 }} \\ \\ \colon\implies{\sf{ x + 600 = 1000 }} \\ \\ \colon\implies{\sf{ x = 1000 - 600 }} \\ \\ \colon\implies{\pmb{\sf\red{ x = 400_{(Fixed \ charge)} }}}$

Hence,

The fixed charges is ₹400 and the cost of food per day is ₹30 For the staying in the hostel.