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Class 9 Exam  >  Class 9 Tests  >  Case Based Questions Test: Pair of Linear Equations in Two Variables - Class 9 MCQ

Case Based Questions Test: Pair of Linear Equations in Two Variables - Class 9 MCQ


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12 Questions MCQ Test - Case Based Questions Test: Pair of Linear Equations in Two Variables

Case Based Questions Test: Pair of Linear Equations in Two Variables for Class 9 2024 is part of Class 9 preparation. The Case Based Questions Test: Pair of Linear Equations in Two Variables questions and answers have been prepared according to the Class 9 exam syllabus.The Case Based Questions Test: Pair of Linear Equations in Two Variables MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Case Based Questions Test: Pair of Linear Equations in Two Variables below.
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Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 1
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Direction: Read the following text and answer the following questions on the basis of the same:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour.

The given problem is based on which mathematical concept

Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 1
The given problem is based on pair of linear equations.
Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 2
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Direction: Read the following text and answer the following questions on the basis of the same:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour.

What is the relative speed of both cars while they are travelling towards each other ?

Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 2
Relative speed of both cars while they are travelling in opposite directions i.e., travelling towards each other = (u + v) km/hr.
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Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 3
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Direction: Read the following text and answer the following questions on the basis of the same:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour.

Q. What are the speeds of the two cars?

Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 3


Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 4
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Direction: Read the following text and answer the following questions on the basis of the same:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour.

Assuming that the speed of first car and second car be u km/h and v km/h respectively.

What is the relative speed of both cars while they are travelling in the same direction ?
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 4
Relative speed of both cars while they are travelling in same direction = (u – v) km/hr.
Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 5
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Direction: Read the following text and answer the following questions on the basis of the same:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What is the difference of speeds in Km/hr of the two cars?
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 5

Let the speed of car at A be x kmph

and the speed of car at B be y kmph

 

when the car travel in same direction Relative Speed is x−y

Dist=100km

t=5 hours

∴  Dist =S×T

100=(x−y)5

x−y=20⟶(I)

 

when car travel in opp direction Relative Speed is x+y

Dist=100km

t=1 hours

Dist=ST

100=(x+y)1

x+y=100⟶(II)

 

Solving (I) & (II)

x−y=20

x+y=100​

   2x=120

x=60km/h

y=40km/h

 

Speed of the car at A =60 km/h

Speed of the car at B=40 km/h

The difference of speeds is 60−40=20

Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 6
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Direction: Read the following text and answer the following questions on the basis of the same:

It is common that Governments revise travel fares from time to time based on various factors such as inflation (a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations.

Situation 2: In a city B, for a journey of 8 km, the charge paid is ₹ 91 and for a journey of 14 km, the charge paid is ₹ 145.

The graph of lines representing the conditions are:
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 6
For situation 2, the lines are

p + 8q = 91

p + 14q = 145

There is not graph which matches both lines.

Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 7
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Direction: Read the following text and answer the following questions on the basis of the same:

It is common that Governments revise travel fares from time to time based on various factors such as inflation (a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations.

Situation 2: In a city B, for a journey of 8 km, the charge paid is ₹ 91 and for a journey of 14 km, the charge paid is ₹ 145.

What will a person have to pay for travelling a distance of 30 km?
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 7
Let fixed charge be Rs x and running charges be Rs y

For the journey of 8km is paid Rs 91

x + 8y = 91

For the journey of 14km the charge paid is Rs145

x + 14y = 145

Using substitution method

we get,

x = 19

y = 9

ATQ,

If a person travels 30km

Total charged = fixed charges + running charges * 30

= 19 + 30 * 9

= 19 + 210

= Rs 289

Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 8
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Direction: Read the following text and answer the following questions on the basis of the same:

It is common that Governments revise travel fares from time to time based on various factors such as inflation (a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations.

Situation 1: In city A, for a journey of 10 km, the charge paid is ₹ 75 and for a journey of 15 km, the charge paid is ₹ 110.

If the fixed charges of auto rickshaw be ₹ x and the running charges be ₹ y km/hr, the pair of linear equations representing the situation is
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 8
According to given situation, we have

x + 10y = 75 ...(i)

x + 15y = 110 ...(ii)

Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 9
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Direction: Read the following text and answer the following questions on the basis of the same:

It is common that Governments revise travel fares from time to time based on various factors such as inflation (a general increase in prices and fall in the purchasing value of money) on different types of vehicles like auto, Rickshaws, taxis, Radio cab etc. The auto charges in a city comprise of a fixed charge together with the charge for the distance covered. Study the following situations.

Situation 1: In city A, for a journey of 10 km, the charge paid is ₹ 75 and for a journey of 15 km, the charge paid is ₹ 110.

A person travels a distance of 50 km. The amount he has to pay is
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 9
Solving two equations,

Now, putting y = 7 in equation (i)

x + 10 × 7 = 75

x + 70 = 75

x = 75 – 70

x = 5

Now, if a person travels a distance of 50 km then, amount = x + 50y

= 5 + 50 × 7

= 5 + 350

= 355

Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 10
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Direction: Read the following text and answer the following questions on the basis of the same:

John and Jivanti are playing with the marbles in the playground. They together have 45 marbles and John has 15 marbles more than Jivanti.

The given problem is based on which mathematical concept ?
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 10
The given problem is based on pair of linear equations.
Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 11
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Direction: Read the following text and answer the following questions on the basis of the same:

John and Jivanti are playing with the marbles in the playground. They together have 45 marbles and John has 15 marbles more than Jivanti.

The number of marbles John had:
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 11
According to the solution of question 1, we get x = 30.
Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 12
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John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. From the quadratic equation to find how many marbles they had to start with, if John had x marbles.
Detailed Solution for Case Based Questions Test: Pair of Linear Equations in Two Variables - Question 12

Given John and Jivanti together have 45 marbles

 

Let the number of Marbles John had be =x

 

Then the number of marbles Jivanti had=45−x

 

Both of them lost 5 Marbles each

Therefore, the number of marbles John had=x−5

 

The number of marbles Jivanti had=45−x−5=40−x

 

Now product of the number of Marbles =124

∴(x−5)(40−x)=124

 

40x−x²−200+5x=124

 

−x²+45x−200−124=0

 

x²−45x+328=0 --- (Multiplying by(-1))

 

By factorization method

 

x2−36x−9x+324=0

x(x−36)−9(x−36)=0

(x−36)(x−9)=0

 

x=36 or x=9

 

When John has 36 Marbles, Jivanti has =45−x=45−36=9 marbles

 

When John has 9 Marbles and Jivanti has =45−x=45−9=36 marbles

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