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

2 Let fraction is x/y

A fraction becomes 1/3 when 1 is subtracted from the numerator

So that

Cross multiply we get

3x -3 = y …(1)

and it becomes 1/ 4 when 8 is added to its denominator

so that

4x = y + 8

Plug the value of y from equation first we get

4x = 3x – 3 + 8

X = 5

Plug this value back in equation first we get

3*5 – 3 = y

15 – 3 = y

12 = y

Hence fraction is x/y = 5/12