Q. 273.9( 7 Votes )

# A part of monthly hostel charges in a college hostel are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay Rs. 4500, whereas a student B who takes food for 30 days, has to pay Rs.5200. Find the fixed charges per month and the cost of the food per day.

Answer :

Let the per day fixed charge of hostel be x.

Excluding fixed charge, a student pays Rs. (4500 - 30x) for 25 days and Rs. (5200 - 30x) for 30 days mess charge

Cost of food per day is given by -

On Cross multiplying, we get -

⇒ 30(4500 - 30x) = 25(5200 - 30x)

⇒ 135000 - 900x = 130000 - 750x

⇒ 150x = 5000

⇒ x = (500/15)

Hence, the fixed charge of hostel per month = (500/15)×30 = Rs. 1000

and, Rate per km = ((4500 - 1000)/25) = (3500/25) = Rs. 140

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSTaxi charges in a city consist of fixed charges and the remaining depending upon the distance travelled in kilometres. If a man travels 80 km, he pays Rs. 1330, and travelling 90 km, he pays Rs.1490. Find the fixed charges and rate per km.NEXTA man invested an amount at 10% per annum and another amount at 8% per annum simple interest. Thus, he received Rs.1350 as annual interest. Had he interchanged the amounts invested, he would have received Rs. 45 less as interest. What amounts did he invest at different rates?

Related Videos

Dealing With the Real Life Problems53 mins

Quiz | Solution of Linear Equations53 mins

Champ Quiz | Consistency and Inconsistency of Solutions36 mins

Pair of Linear Equations in Two Variables46 mins

Quiz | Real Life Problems Through Linear Equations56 mins

Smart Revision | Important Word Problems37 mins

Dealing with the Real Life Problems54 mins

Elimination (quicker than quickest)44 mins

Bonus on Applications of Linear Equations in Two Variables43 mins

Consistent and Inconsistent Equations33 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Solve the following pairs of equations

NCERT - Maths Exemplar

Solve for x and y:

RS Aggarwal - MathematicsSum of the areas of two squares is 400 cm^{2}. If the difference of their perimeters is 16 cm, find the sides of the two squares.