The document Value Based Questions (VBQs) - Linear Equations in Two Variables Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by VP Classes.

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**Question 1. Kamaruddin is a rikshaw-puller. He charges **â‚¹**10 for the first kilometre and @ **â‚¹** 4 per kilometre for subsequent distance covered:****(i) Write the linear equation to express the above statement.****(ii) Draw the graph of the linear equation so obtained on a cartesian plane.****(iii) By using a manually operated rikshaw (instead of an autorikshaw), which value is depieted by Kamaruddin?****Solution. **(i) Let the total distance covered be x km and the fare charged â‚¹ y.

âˆ´ Fare for first kilometre = â‚¹10

Remaining distance = (x â€“ 1) km

â‡’ Fare for the remaining distance = â‚¹ 4 (x â€“ 1)

âˆ´ Total fare = â‚¹ 10 + â‚¹ 4 (x â€“ 1)

= â‚¹ [10 + 4 (x â€“ 1)]

Thus, the required equation is:

y = 10 + 4 (x â€“ 1) = 10 + 4x â€“ 4 = 4x + 6

or

y â€“4x = 6

(ii) To draw the graph, we use the following table: y â€“ 4x = 6

x | 0 | -1 | -2 |

y | 6 | 2 | -2 |

(x,y) | (0,6) | (-1, 2) | (-2,-2) |

Plot the points (0, 6), (â€“1, 2) and (â€“2, â€“2). Join the points. The line AB is the required graph.

(iii) Promoting pollution free environment.

**Question 2. Savitaâ€™s car broke down at a point 2 units away from the garage. She requested a man for help, who pushed her car to the garage. The work done by a body on application of a constant force is the product of the constant force and the distance travelled by the body in the direction of force.****(i) Express the above activity in the form of a linear equation in two variables by taking the constant force as 3 units and distance travelled as 2 units.****(ii) Verify it by plotting the graph.****(iii) By pushing the car to the garage, which value is depicted by the man?****Solution.** (i) Work done = (constant force) Ã— (distance)

Let workdone be y (units) and distance travelled be x (unit), keeping the force as constant 3 units.

âˆ´ y = 3x which is the required linear equation in variables x and y.

(ii) To plot the graph of linear equation y = 3x,

we need at least two ordered pairs satisfying the equation.

Here, we have : x = 0, y = 0 and x = 1, y = 3.

i.e., ordered pairs (0, 0) and (1, 3) satisfy the equation y = 3x.

Now, we plot the points A (0, 0) and B (1, 3) and join AB as shown below:

**Note:** Here, we have not taken the negative side of the graph, because work done cannot be negative.

To verify the graph, draw a perpendicular to xâ€“axis at (2, 0) meeting the graph AB at the point C.

The co-ordinates of C are (2, 6).

It verifies that the workdone = 6 units.

(iii) Co-operation.**Question 3. A and B, two students of class IX of a school, together contributed **â‚¹**100 towards The Prime Ministerâ€™s Relief Fund to help the earthquake victims.****(a) Write a linear equation which the above data satisfies.****(b) Draw the graph for the above data.****(c) Which mathematical concept is used in the above problem?****(d) By donating towards Prime Ministerâ€™s Relief Fund, which value is depicted by A and B?****Sol. **(a) Let the contribution made by â€˜Aâ€™ = â‚¹ x

And the contribution made by â€˜Bâ€™ = â‚¹ y

Since, the total contribution made by A and B = â‚¹100

âˆ´ We have x + y = 100

(b) To draw the graph of x + y = 100 we prepare the following table :

x | 0 | 10 | 40 | 90 |

y | 100 | 90 | 60 | 10 |

(x,y) | (0,100) | (10,90) | (40,60) | (90,10) |

Draw x-axis and y-axis, plotting the points (0, 100), (10, 90), (40, 60) and (90, 10) and then joining them, we get a straight line PQ as shown here.

The st. line PQ represents the above data.

(c) Linear Equations in two variables.

(d) Helping the needy persons.**Question 4. The taxi fare in a town is **â‚¹** 15 for the first kilometre and **â‚¹ **10 per kilometre for the subsequent distance.****(a) Taking the distance as â€˜xâ€™ km and total fare as **â‚¹ **y, write a linear equation for the above information.****(b) Deepak hired a taxi for 10 km and paid **â‚¹** 200 for it. He asked the taxi-driver to donate the balance to an orphanage. What amount will the taxi-driver donate to the orphanage?****(c) Which mathematical concept is involved in the above problem?****(d) By asking the taxi-driver to donate the balance to an orphanage, which value is depicted by Deepak?****Sol.** (a) Total distance covered = x km

Total taxi fare for â€˜xâ€™ km = â‚¹ y

Taxi fare for first km = â‚¹ 15

Remaining distance = (xâ€“1) km

Fare for (x â€“ 1) km = â‚¹ 10 Ã— (xâ€“1)

âˆ´ Total fare = â‚¹10 (xâ€“1) + 15

â‡’ 10 (x â€“ 1) + 15 = y

Which is the required equation representing the above problem . ...(1)

(b) Substituting x = 10 in the above equation (1), we get 10 (10 â€“ 1) + 15 = y

â‡’ 100 â€“ 1 + 15 = y

â‡’ 90 + 15 = y

â‡’ y = â‚¹ 105

As Deepak paid â‚¹200,

âˆ´ Balance amount = â‚¹200 â€“ â‚¹ 105 = â‚¹ 95

âˆ´ Donation to orphanage = â‚¹ 95

(c) Linear equations in two variables.

(d) Charity.**Question 5. In a one-day cricket match, the organiser decided to donate as much money to an â€˜old -age homeâ€™ as the run scored by the first pair of batsman. Ratan and Naval were the opener batsman. They together scored â€˜Nâ€™ runs such that for every 1 run of Ratan, Naval scored 3 runs.****(a) Set up a linear equation with â€˜xâ€™ and â€˜yâ€™ representing the number of runs of Ratan and Naval respectively.****(b) Find the number of runs scored by Ratan, if Naval scored 180 runs.****(c) If Ratanâ€™s score is 99, then what amount of money will be donated to the old-age home by the organiser?****(d) Which mathematical concept is used in the above problem?****(e) By making donation to the old-age home, which value is depicted by the organiser?****Sol. **(a) Number of runs scored by Ratan = x

âˆ´ Number of runs scored by Naval = y = 3x

[âˆµ For every 1 run of Ratan, Naval scored 3 runs]

âˆµ Total number of runs scored together by the opener batsman = N

âˆ´ x + y =N

(b) âˆµ Number of runs scored by Naval = 180

âˆ´ y = 180

Since,

y =3x

â‡’ 3x = 180

â‡’ x = (180/3) = 60

â‡’ Score of Ratan = 60

(c) âˆµ Number of runs scored by Ratan, x =99

âˆ´ Number of runs scored by Naval, y =3x = 3 Ã— 99 = 297

Now, x + y =N

âˆ´ N = 99 + 297 = 396

âˆ´ Organisers will donate â‚¹ 396 to the â€˜old age homeâ€™.

(d) Linear equations in two variables.

(e) Helping the aged persons.

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