Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.4 Solutions Two Variables, One Line

Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.4 Solutions – Two Variables, One Line help students understand the concept of slope and how it describes the steepness of a line. This exercise covers finding slope from graphs, comparing slopes, and applying the concept of rise and run in practical situations such as ramps and inclined surfaces.

The step-by-step solutions make it easier to interpret linear graphs and strengthen conceptual understanding. Students can also refer to the Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.4 Solutions PDF for convenient revision and exam preparation.

Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.4 Solutions Two Variables, One Line

NCERT Class 9 Maths Ganita Manjari Chapter 13 Exercise Set 13.4

1. On two different days a family buys movie tickets and snack boxes. Let the cost of one movie ticket be ₹x and the cost of one snack box be ₹y. Frame a pair of linear equations in x and y to represent the following situations:

(i) On the first day, the family buys 2 movie tickets and 3 snack boxes for ₹850.
(ii) On the second day, the family buys 4 movie tickets and 1 snack box for ₹1100.

Answer:

Let:

₹x = cost of one movie ticket
₹y = cost of one snack box

(i)

Cost of 2 movie tickets and 3 snack boxes is ₹850.

Therefore,

2x + 3y = 850

(ii)

Cost of 4 movie tickets and 1 snack box is ₹1100.

Therefore,

4x + y = 1100

Hence, the required pair of linear equations is:

2x + 3y = 850
4x + y = 1100

2. Two friends, Sahil and Meena, travelled by taxi. Let the fixed charge for one taxi trip be ₹x and the additional charge per kilometre be ₹y. Frame a pair of linear equations in x and y to represent the following situation:

(i) Sahil travelled 6 km and paid a total fare of ₹122.
(ii) Meena travelled 8 km and paid a total fare of ₹160.

Answer:

Let:

₹x = fixed charge for one taxi trip
₹y = additional charge per kilometre

For Sahil:

x + 6y = 122

For Meena:

x + 8y = 160

Hence, the required pair of linear equations is:

x + 6y = 122
x + 8y = 160

3. In a sports meet, tickets for adults cost ₹150 each and tickets for children cost ₹100 each. A total of 200 people attended the meet, and the total amount collected from ticket sales was ₹25,000. (Let the number of adult tickets sold be x and the number of children’s tickets sold be y.) Frame a pair of linear equations in x and y to represent this situation.

Answer:

Let:

x = number of adult tickets sold
y = number of children’s tickets sold

Since a total of 200 people attended:

x + y = 200

The total amount collected was ₹25,000:

150x + 100y = 25,000

Hence, the required pair of linear equations is:

x + y = 200
150x + 100y = 25,000

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