4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

 (i) 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 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.

Let fixed charge = Rs x

Variable charge  = Rs y per day

When a student Atakes food for 20 days she has to pay Rs 1000 as hostel charges

So we get

X  + 20 y = 1000       …(1)

Subtract 20 y both side we get

X = 1000 – 20 y        …(2)

who takes food for 26 days, paysRs 1180 as hostel charges

we get

x + 26 y = 1180

plug the value of x we ge t

1000 – 20 y + 26y = 1180

6y = 180

Y = 180/6 = 30

Plug the value of y in equation second we get

X = 1000 – 20 * 30

X = 1000 – 600

X = 400

Hence fixed charge x  = Rs 400

And variable charge y = Rs 30