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

Advertisements
Advertisements

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

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.

Advertisements

Solution

Let x be the fixed charge of the food and y be the charge for food per day.

According to the question,

x + 20y = 1000 ... (i)

x + 26y = 1180 ... (ii)

Subtracting equation (i) from equation (ii), we get

6y = 180

y = 180/6 = 30

Putting this value in equation (i), we get

x + 20 × 30 = 1000

x = 1000 - 600

x = 400

Hence, fixed charge = Rs 400 and charge per day = Rs 30

  Is there an error in this question or solution?
Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.5 [Page 63]

APPEARS IN

NCERT Mathematics Class 10
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 4.1 | Page 63

RELATED QUESTIONS

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?


A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.


A thief runs with a uniform speed of 100 m/minute. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/minute every succeeding minute. After how many minutes the policeman will catch the thief.


A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?


For which values of a and b does the following pair of linear equations have an infinite number of solutions?

2x + 3y = 7

(a – b) x + (a + b) y = 3a + b – 2


Solve the following systems of equations:

4u + 3y = 8

`6u - 4y = -5`


Solve the following systems of equations:

`4/x + 3y = 14`

`3/x - 4y = 23`


Solve each of the following systems of equations by the method of cross-multiplication 

`x/a + y/b = 2`

`ax - by = a^2 - b^2`


Solve each of the following systems of equations by the method of cross-multiplication :

`ax + by = (a + b)/2`

3x + 5y = 4


Solve each of the following systems of equations by the method of cross-multiplication :

`57/(x + y) + 6/(x - y) = 5`

`38/(x + y) + 21/(x - y) = 9`


Solve each of the following systems of equations by the method of cross-multiplication :

6(ax + by) = 3a + 2b

6(bx - ay) = 3b - 2a


Solve each of the following systems of equations by the method of cross-multiplication :

`a^2/x - b^2/y = 0`

`(a^2b)/x + (b^2a)/y = a + b, x , y != 0`


Solve the system of equation by using the method of cross multiplication:
`5/("x+y") - 2/("x− y") + 1 = 0, 15/("x+y") + 7/("x− y") – 10 = 0`


Solve the system of equations by using the method of cross multiplication:
`(ax)/b- (by)/a – (a + b) = 0, ax – by – 2ab = 0`


If  `|( 4,5), (m , 3)|` = 22, then find the value of m.


Complete the activity to find the value of x.
3x + 2y = 11 …(i) and 2x + 3y = 4 …(ii)
Solution:
Multiply equation (i) by _______ and equation (ii) by _______.
`square` × (3x + 2y = 11)    ∴ 9x + 6y = 33 …(iii)
`square` × (2x + 3y = 4)      ∴ 4x + 6y = 8   …(iv)
Subtract (iv) from (iii),
`square` x = 25
∴ x = `square`


Solve 0.4x + 0.3y = 1.7; 0.7 x − 0.2y = 0.8


Share
Notifications



      Forgot password?
Use app×