Question

A part of monthly hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for 25 days, she has to pay ₹ 4,500 as hostel charges whereas Mansi who takes food for 30 days pays ₹ 5,200 as hostel charges. Find the fixed charges and the cost of food per day.​

Answer 1

$\rm{ \large{ \rm \: Solution}}$

Let assume that

Fixed per month charges be ₹ x

and

Per day mess charges be ₹ y.

According to first condition

When Swati takes food for 25 days, she has to pay ₹ 4,500 as hostel charges.

So, it implies,

Fixed charges = ₹ x

Mess charges for 25 days = ₹ 25y

$\longmapsto \rm \: x + 25y = 4500 - - - (1)$

According to second condition,

Mansi who takes food for 30 days pays ₹ 5,200 as hostel charges.

So, it implies,

Fixed charges = ₹ x

Mess charges for 30 days = ₹ 30y

$\longmapsto \rm \: x + 30y = 5200 - - - - (2)$

On subtracting equation (1) from equation (2), we get

$\longmapsto \rm \: 5y = 700$

$\longmapsto \rm \: y = 140$

On substitute y = 140 in equation (1), we get

$\longmapsto \rm \: x + 25 \times 140 = 4500$

$\longmapsto \rm \: x + 3500 = 4500$

$\longmapsto \rm \: x = 4500 - 3500$

$\implies \bf \: x = 1000$

Hence,

Fixed per month charges be ₹ 1000

and

Per day mess charges be ₹ 140