CHAPTER - 3: PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

MCQ: 1 MARK EACH

1. The pair of equations y = 0 and y = –7 has
(a) one solution (b) two solution. (c) infinitely many solutions (d) no solution
2. The pair of equations x = a and y = b graphically represents the lines which are
(a) parallel (b) intersecting at (a, b) (c) coincident (d) intersecting at (b, a)
3. The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
(a) 3 (b) – 3 (c) – 12 (d) no value
4. When lines l1 and l2 are coincident, then the graphical solution of the linear equations have
(a) infinite number of solutions (b) unique solution (c) no solution (d) one solution
5. When lines l1 and l2 are parallel, then the graphical solution system of linear equation have
(a) infinite number of solutions (b) unique solution (c) no solution (d) one solution
6. The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has
(a) infinite number of solutions (b) unique solution (c) no solution (d) one solution
7. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(a) infinite number of solutions (b) unique solution (c) no solution (d) one solution
8. The sum of the digits of a 2-digit number is 9. If 27 is added to it, the digits of the no. get reversed. The no. is
(a) 36 (b) 72 (c) 63 (d) 25
9. If a pair of equation is consistent, then the lines will be
(a) parallel (b) always coincident (c) always intersecting (d) intersecting or
coincident
10. The solution of the equations x + y = 14 and x – y =4 is
(a)x = 9 and y = 5 (b) x = 5 and y = 9 (c) x = 7 and y = 7 (d) x = 10 and y = 4
11. The value of k for which the system of equations x – 2y = 3 and 3x + ky = 1 has a unique solution is
(a) k = – 6 (b) k ≠ – 6 (c) k = 0 (d) no value
12. If a pair of equation is inconsistent, then the lines will be
(a) parallel (b) always coincident (c) always intersecting (d) intersecting or coincident
13. The value of k for which the equations 2x + 3y = 5 and 4x + ky = 10 has infinite many solution is
(a) k = – 3 (b) k ≠ – 3 (c) k = 0 (d) none of these
14. The value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution is
(a) k ≠ – 3 (b) k ≠ 3 (c) k ≠ 0 (d) k≠ –1
15. Sum of two numbers is 35 and their difference is 13, then the numbers are
(a) 24 and 12 (b) 24 and 11 (c) 12 and 11 (d) none of these
16. The solution of the equations 0.4x + 0.3y = 1.7 and 0.7x – 0.2y = 0.8 is
(a) x = 1 and y = 2 (b) x = 2 and y = 3 (c) x = 3 and y = 4 (d) x = 5 and y = 4
17. The solution of the equations x + 2y = 1.5 and 2x + y = 1.5 is
(a) x = 1 and y = 1 (b) x = 1.5 and y = 1.5 (c) x = 0.5 and y = 0.5 (d) none of these
18. The value of k for which the system of equations x + 2y = 3 and 5x + ky + 7 = 0 has no solution is
A) 10 (b) 6 (c) 3 (d) 1
19. Sum of two numbers is 50 and their difference is 10, then the numbers are
(a) 30 and 20 (b) 24 and 14 (c) 12 and 2 (d) none of these
20. The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digit
exceeds the given number by 18, then the number is
(a) 72 (b) 75 (c) 57 (d) none of these

Answers:
1) d) 2) b) 3) d) 4) a) 5) c)
6) a) 7) c) 8) a) 9) d) 10) a)
11) b) 12) a) 13) d) 14) b) 15) b)
16) b) 17) b) 18) a) 19) a) 20) c)
ASSERTION AND REASONING QUESTIONS : 1 MARK EACH
DIRECTIONS-
A statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Q1-Assertion: The graphical representation of x + 2y - 4 = 0 and 2x + 4y - 12 = 0 will be a pair of parallel lines.

Reason: Let a1x+b1y+c1=0 and a2x+b2y+c2=0 be two linear equations and if a1/a2=b1/b2≠c1/c2, then the pair of
equation represents parallel lines and they have no solution.
Q2-Assertion : The pair of equations 3x−4y−1=0 and 2x−8/3y+5=0 is inconsistent.
Reason : The pair of equations 3x−4y−1=0and 2x−8/3y+5=0 has no solution.
Q3-Assertion : A student found the two lines 4x - y - 8 = 0 and 2x - 3y + 6 = 0 to be consistent.
Reason : The pair of linear equations x - 2y = 3 and 3x + 4y =20 when solved, results exactly in one solution.
Q4-Assertion : A pair of linear equations has no solution then the graphical representation is parallel lines.
Reason : If two lines are intersecting then, they have no solution pair of linear equations is inconsistent.
Q5-Assertion: The value of q=±2, if x=3, y=1 is the solution of the line 2x+y-q 2-3=0.
Reason: The solution of the line will satisfy the equation of the line.
Q6-Assertion: The value of k for which the equations kx-y=2 and 6x-2y=3 has a unique solution is 3.
Reason: The graph of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 gives a pair of intersecting lines
if a1/a2 ≠ b1/b2
Q7-Assertion: The graph of the equation of the form y=mx is a line which always passes through the origin.
Reason: A linear equation in two variables has infinitely many solutions.
Q8-Assertion : The equation 5x – 25 = 55 is considered to have One Variable only.
Reason : A linear equation in two variables has infinite solution
Q9-Assertion : Two lines given by 2x + 5y = 4 and x - 2.5y = 2, when constructed on a graph are coincident.
Reason : Two lines given by 2x + 5y = 4 and x - 2.5y = 2, when solved results in a unique solution.
Q10-Assertion (A): The pair of linear equations x + y = 1 & 2x + 2y = 2 is inconsistent.
Reason (R): If a1/a2=b1/b2=c1/c2, then the pair of equations is consistent (dependent).
Q11-Assertion: If a pair of linear equations is consistent, then the lines are intersecting or coincident
Reason: The pair of linear equation in two variables definitely have a solution.
Q12-Assertion: If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then the value of k is 4
Reason: The condition for parallel lines is a1/a2 = b1/b2 ≠ c1/c2
Q13-Assertion: The point (0, 4) lies on the graph of the linear equation 4x + 4y = 16
Reason: (0, 4) satisfies the equation 4x + 4y = 16.
Q14-Assertion : The graph of the linear equation x – 5y = 1 passes through the point (6, 1).
Reason: Every point lying on graph is not a solution of x – 5y = 1.
Q15-Assertion (A): The pair of linear equations x + y = 1 & x + 2y = 5 has infinite solutions.
Reason (R): If a1/a2≠b1/b2, then the pair of equations is intersecting and has a unique solution
Q16-Assertion (A): The pair of linear equations x + y = 1 & x + y = 5 is parallel to each other.
Reason (R): If a1/a2=b1/b2≠c1/c2, then the pair of equations is parallel and has a unique solution.
Q17- Assertion :For the given figure x + y = 14 and x−y= 30
Reason : In rectangle all sides are of equal length.
Q18-Assertion: If x=2, y=1 is the soln. of eqn. 2x + 3y = k, then k = 7
Reason: The solution of an equation satisfies the equation.
Q19-Assertion :If x = 2k - 1 and y = k is the solution of the equation
3x - 5y = 7 then k = 10
 Reason: The linear equation in two variables has infinite solution.
Q20-Assertion: x = 5 is equation of a line parallel to Y axis
Reason: The equation of a line parallel to Y axis is x=a.
ANSWERS:

Q1 A Q6 A Q11 C Q16 C

Q2 B Q7 B Q12 D Q17 C

Q3 B Q8 B Q13 A Q18 A

Q4 C Q9 D Q14 C Q19 B

Q5 A Q10 D Q15 D Q20 A

VERY SHORT ANSWER TYPE QUESTIONS: 2 marks each

1. Find the value of k, so that the system of equations 3x – y – 5 = 0; 6x – 2y – k = 0. has no solution:
2. Find the value of k, so that the following system of equations has infinitely many solution:
3x + 5y = 4; kx + 10y = 8.
Find the value of k, so that the following system of equations has no solution:
3. 3x + y = 1; (2k – 1)x + (k – 1) y = (2k – 1).
4. x – 2y = 1; (2k + 3)x + (k – 1) y = (2k + 5).
5. x - 2 y = 3; 3x + ky = 1.
6. x + 2 y = 5; 3x + ky +15 = 0.
7. kx + 2 y = 5; 3x - 4 y = 10.
8. x + 2 y = 3; 5x + ky + 7 = 0.
9. 8x + 5 y = 9; kx +10 y = 15.
10. (3k +1)x + 3y - 2 = 0; (k 2 +1)x + (k - 2)y - 5 = 0.
11. kx + 3y = 3; 12x + ky = 6.

Find the value of k, so that the following system of equations has a unique solution:
12. x - 2 y = 3; 3x + ky = 1.
13. x + 2 y = 5; 3x + ky +15 = 0.
14. kx + 2 y = 5; 3x - 4 y = 10.
15. x + 2 y = 3; 5x + ky + 7 = 0.
16. 8x + 5 y = 9; kx +10 y = 15.
17. kx + 3y = (k - 3); 12x + ky = k.
18. kx + 2 y = 5; 3x + y = 1.
19. x - 2 y = 3; 3x + ky = 1.
20. 4x - 5 y = k; 2x - 3y = 12.

Answers:
1. k ≠ 10 2. K = 6 3. K = 2 4. K = –1
5. k = –6 6. K = 6 7. K = –3/2 8. K= 10
9. k = 16 10. K = –1 11. K = ±6 12. K ≠ –6
13. K ≠ 6 14. K ≠ –3/2 15. K ≠ 10 16. K ≠ 16
17. K ≠ ±6 18. K ≠ 6 19. K ≠ -6 20. K can have any integer value.

SHORT ANSWER TYPE QUESTIONS (3 MARK EACH)

1. Solve the following pair of linear equations for x and y: 141x + 93y = 189; 93x + 141y = 45
2. Solve for x and y: 27x + 31y = 85 and 31x + 27y = 89
3. Solve the following pair of equations: 49x + 51y = 499 and 51x + 49y = 501
 4.Solve by elimination method: 3x = y + 5 and 5x – y = 11
5.Solve by elimination: 3x – y – 7=0 and 2x + 5y + 1 = 0
6.Find the two numbers whose sum is 75 and difference is 15.
7.Solve 2x + 3y = 11 and 2x – 4y = –24 and hence find the value of ‘m’ for which y = mx + 3
8.Solve the following pair of linear equations by the elimination method: x + 2y = 2; x – 3y = 7
9.The sum of a two-digit number and the number obtained by reversing the order of its digits is 165. If the
digits differ by 3, find the number.
10. The sum of the digits of a two digit number is 8 and the difference between the number and that formed
by reversing the digits is 18. Find the number.
11. The coach of a cricket team buys 3 bats and 6 balls for₹ 3900. Later, she buys another bat and 3 more
balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.
12. The cost of 2 kg of apples and 1 kg of grapes on a day was found to be 160. After a month, the cost of 4 kg
of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically
ANSWERS:
1. x=2,Y=–1 6. X = 45, Y = 30
2. x = – 1 , Y= – 2. 7. X = – 2, Y = 5
3. x = 29/2, Y = – 9/2 8. X = 4, Y = – 1
4. x = 3, Y = 4 9. X = 9, y = 6, thus number will be 69 or 96.
5. X = 2, Y = – 1 10. X = 5 ,y = 3, thus number will be 53

LONG ANSWER TYPE QUESTIONS (5 MARKS EACH)

1. Solve the following system of linear equations graphically: 3x + y – 11 = 0 and x – y = 1. Find the area of
triangle so formed between these lines and y – axis.
2. Draw the graph of the pair of equations 2x + y = 4 and 2x – y = 4. Write the vertices of the triangle formed by
these lines and the y – axis. Find the area of this triangle.
3. Two years ago, Dev was thrice as old as his daughter. Six years later, he will be four years older than twice her
age. How old are they now?
4. There are some students in the two examination halls A and B. To make the number of students equal in each
hall, 10 students are sent from A to B. But if 20 students are sent from B to A, the number of students in A
becomes double the number of students in B. find the number of students in each hall.
5. A two-digit number is obtained either by multiplying the sum of the digits by 8 and then subtracting 5 or by
multiplying the difference of the digits by 16 and then adding 3. Find the number.
6. A railway half ticket cost the half of the full fare but the reservation charges are the same on a half ticket as on
a full ticket. One reserved first class ticket from the stations A to B costs ₹ 2530. Also, one reserved first class
ticket and one reserved first class half ticket from station A to station B costs ₹ 3810. Find the full first class
fare from stations A to B and also the reservation charges.
7. A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum ₹1008. If she had
sold the saree at 10 % profit and the sweater at 8 % discount, she would have got ₹1028. Find the list price of
the saree and sweater ( before discount and profit)
8. Jaya had some bananas and she divided them into two lots A and B. she sold the first lot at the rate of ₹2 for 3
bananas and the second lot at the rate of ₹1 per banana and got a total of ₹400. If she had sold at the rate of
₹1 per banana and the second lot at the rate of ₹4 for 5 bananas, her total collection would have been ₹ 460.
Find the total number of bananas she had.
9. A fraction becomes ½ when 1 is added to both numerator and denominator. It reduces to 2/5 if 1 is subtracted
from both numerator and denominator. Find the fraction.
10. Jiya scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong
answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect
answer, then Jiya would have scored 50 marks. How many questions were there in the test?
11. For what values of a and b will the equations 3x + 4y – 12 = 0 and (a + b) x + 2(a – b) y – (5a – 1) = 0 will have
an infinite number of solutions?
12. If 3 times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the
remainder. If 5 times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder.
Find the numbers.
13. The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the
numerator and denominator are increased by 3 , they are in the ratio 2:3. Determine the fraction.
14. The monthly incomes of A and B are in the ratio 5:4 and their monthly expenditures are in the ratio 7:5. If
each saves ₹9000 per month, find the monthly income of each.
15. A train covered a certain distance at a uniform speed. If the train had been 5kmph faster, it would have taken
3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours
more than the scheduled time. Find the length of the journey.
Answers:
1. X = 3 , y = 2 : area of triangle = ½ x 12 x 3 = 18 sq units
2. Vertices are ( 0,4) , (2,0), ( 0, -4) , area = 8 sq units.
3. Dev’s age = x and his daughter’s age = y, Equations are x – 3y = -4 and x – 2y = 10
Ans. Ages of Dev and his daughter are 38 years and 14 years
4. If the number of students in halls A and B are x and y, equations are formed as x – 2y = - 60, x – y = 20.
Solution is x = 100, y = 80
5. Let the two digit number is 10x + y, Equations are 2x – 7y = -5 and 6x – 17 y = -3
X = 8 , y = 3 number is 83
6. Let the cost of one full class ticket be ₹ x and reservation charges be ₹y per ticket.
Equations are x + y = 2530 and x + y + x/2 + y = 3810 ,
Solution is x = 2500 , y = 30, Ticket cost = ₹2500 and reservation charges = ₹30
7. Let the price of saree and sweater are ₹ x and y , Equations are 108% of x + 90% of y = 1008
108x + 90 y = 100800 and 110x + 92 y = 102800, solution is ₹ 600 and ₹400
8. Let the number of bananas in lots A and B are x and y . Equations are 2/3 x + y = 400 and x + 4/5 y = 460.
Solution is x = 300 and y = 200. Total number of bananas is 500.
9. Let the fraction is x/y, Equations are 2x – y = -1 and 5x – 2y = 3
The solution is x = 5, y = 11, fraction is 5/11
10. Let the number of right answer is x and wrong answers is y. equations are 3x – y = 40 and 4x – 2y = 50.
X = 15, y = 5
11. A = 5, b = 1
12. Equations are 3x – 4y = 8 and – 3x + 5y = 5, Solution is 20, 13
13. Let the fraction is x/y , Equations are y – x = 4 and 2y – 3x = 3. Fraction is 5/9
14. ₹30000 and ₹ 24000
15. Let the original speed of the train be x kmph and the time taken to complete the journey = y hrs.
So the length of the whole journey = xy
Case 1 : Speed = x + 5, time taken = y – 3 : (x+ 5) (y – 3) = xy
Case 2: (x – 4)(y + 3) = xy
On solving x = 40 , y = 27, Length of journey = 40 x 27 = 1080 km
CASE STUDY BASED QUESTION ( 4 marks each)
Case Study 1: Riya's Bookstore Purchase: Riya and Priya bought stationery from the same bookstore. The total
cost of their purchases was recorded, and the following data was provided:
Riya bought 3 notebooks and 2 pens for ₹80. Priya bought 2 notebooks and 3 pens for ₹70.
Let cost of one notebook is Rs x and cost of one pen is Rs y,
Based on the given information answer the following question:
i) What algebraic equation represents Riya’s purchasing
ii) What algebraic equation represents Priya’s purchasing.
iii) What is the cost a notebook and a pen.
Or What is the cost 5 notebook and 2 pen.

Case Study 2: Car Rental Service

A car rental company charges a fixed amount for renting a car plus an additional charge per km travelled. The
cost of two different trips was recorded:
For a 10 km trip, the cost is ₹800. For a 15 km trip, the cost is ₹950. Let fix charge be Rs x and additional charge
Rs.y per km, Based on the given information answer the following question:
i) Formulate the linear equations representing the Ist situation.
ii) Formulate the linear equations representing the IInd situation.
iii) What is the fixed charge and the additional fee per kilometer rate.
OR If the fixed charge is increased by ₹50, calculate the new total cost for a 20 km trip.

Case Study 3: Ticket Counter on Bus Stand:

From Bengaluru bus stand, if Riddhima buys 2 tickets to Malleswaram and 3 tickets to Yeswanthpur, then total
cost is ₹46; but if she buys 3 tickets to Malleswaram and 5 tickets to Yeswanthpur, then total cost is ₹74.
Consider fares from Bengaluru to Malleswaram and that to Yeswanthpur as ₹x and ₹y
respectively . Based on the above information answer the following questions.
(i) Represent the equation for first condition.
ii) What is the equation for second situation.
iii) What is the fare from Bengaluru to Malleswaram and Bengaluru to Yeswanthapur.
or if Ridhima buy four-four tickets of both type, what amount she pay?
Case Study 4 -Hostel Monthly Charges
A part of monthly hostel charges in a college is fixed and the remaining depends on the number of days one has
taken food in the mess. When a student Anu takes food for 25 days, she has to pay Rs4500 as hostel charges,
whereas another student Bindu who takes food for 30 days, has to pay Rs5200 as hostel charges.
Considering the fixed charges per month by ₹x and the cost of food per day by ₹y, then answer the following
questions.
(i)Represent algebraically the situation faced by both Anu and Bindu.
(ii) What is the cost of food per day?
(iii) What is the fixed charges per month for the hostel ?
Or If Bindu takes food for 20 days, then what amount she has to pay?

Case study 5: National Highway Points A and B representing Chandigarh and Kurukshetra respectively are
almost 90 km apart from each other on the highway
A car starts from Chandigarh and another from Kurukshetra at the same time. If these cars go in the same
direction, they meet in 9 hours and if these cars go in opposite direction they meet in 9/7 hours. Let X and Y be
two cars starting from points A and B respectively and their speed be x km/hr and y km/hr respectively.
 Based on the above information answer the following questions-
i) When both cars move in the same direction, then what is the algebraic equation for Ist situation.
(ii) When both cars move in opposite direction, then what is the algebraic equation for IInd situation.
(iii) What is the Speed of car X and car Y.
Or If speed of car X and car Y, each is increased by 10 km/hr, and cars are moving in opposite direction,
then after how much time they will meet?
Case Study - 6
General form of pair of linear equation in two variable is a1x+b1y+c1=0 and a2x +b2y+c2=0.
If graph of pair of linear equations represent two intersecting lines, then point of intersection is the solution of
pair of linear equations.
If graph represent two parallel lines then pair of linear equation has no common solution.
If graph represent to coincident lines then pair of linear equation has infinitely many solution.
Based on given information answer the following questions-
i) The pair of equation x=5 and y=5 graphically intersect at which point?
ii) For the linear equation 2x + 5y – 8 = 0, find a linear equation in two variable such that the graphical
representation of the pair so formed represents parallel lines.
iii) The graph of linear equation x=3 and x=5 and 2x – y – 4 = 0 and x-axis represent which type of figure?
Or Find the area of the region formed by lines x=2, y=5, x=0 and y=0.
Case study -7
Teacher and students of class x of a school had gone to Nandan Kanan Zoological Park for study tour. After
visiting different places of Nandan Kanan, lastly, they visited
bird’s sanctuary and deer park.
Rohan is a clever boy and keen observer. He put the question to
his friends “How many birds are there and how many deer are
there (at particular time) in Nandan Kanan?” Rahul’s friends,
Nishith gave the correct answer as follow :
‘Nishith answered that total animals have 1000 eyes and 1400
legs’.
i) If x and y be the number of bird and deer respectively,
what is the equation of total number of eyes?
ii) What is the equation of total numbers of legs?
iii) How many birds are there in the zoo?
Or What is the total number of animals (birds and deer) in the zoo.
Case study -8
Deepak and Sanju works together in a bank in Delhi. Home town of both of them is Rampur in UP which is at a
distance of 300km from Delhi.
To reach Rampur from Delhi they travel partly by train and partly by bus. This Diwali they travelled separately
to Rampur. Deepak travels 60 km by train and remaining by bus and taken 4 hrs. Sanju travels 100km by train
and remaining by bus and takes 4 hrs10 minutes.
Based on given information answer the following questions:
i) If speed of the train is x km/h and speed of bus is y km/h then write algebraic representation of the
situation.
ii) Find the speed of the bus.
iii) If speed of the train is 90 km/h and speed of bus is 60 km/h then find time taken by Deepak to travel 60
km by train and 240 km by bus.
Or If speed of the train is 120 km/h and speed of bus is 60 km/h then find time taken by Sanju to travel
120 km by train and 180 km by bus.
 Case study -9
An alumni association is an association of former students. These associations often organize social events,
publish newsletters or magazines and raise funds for the organisation. The alumni meet of two batches of a
college- batch A & batch B were held on the same day in the same hotel in two separate halls “Rose” and
“Jasmine”. The rents were the same for both the halls. The expense for each hall is equal to the fixed rent of
each hall and proportional to the number of persons attending each meet. 50 persons attended the meet in
“Rose” hall, and the organisers had to pay ₹ 10000 towards the hotel charges. 25 guests attended the meet in
“Jasmine” hall and the organisers had to pay ₹ 7500 towards the hotel charges. Denote the fixed rent by ₹ x
and proportional expense per person by ₹ y.
(i) Represent algebraically the situation in hall “Rose”.
(ii) Represent algebraically the situation in hall “Jasmine”
(iii) What is the fixed rent of the halls?
OR Find the amount the hotel charged per person.
Case study-10
Two friends Raj and Anuj have to travel to Shimla via Chandigarh from Gurgaon. when they reached the bus
stand of Gurgaon, raj got a call from his friend Ankit who was also on his way to bus stand. Ankit requested
raj to buy two tickets to Chandigarh and 3 tickets to Shimla also Anuj’s friend Kamal asked Anuj to buy 3
tickets to Chandigarh and 4 tickets to Shimla. Raj purchased 2 tickets to Chandigarh and 3 tickets to Shimla
for Rs 3700, Anuj spent Rs 5100 to buy 3 tickets to Chandigarh and 4 tickets to Shimla.
(1) if cost of one ticket Gurgaon to Chandigarh is Rs X and cost of one ticket Gurgaon to Shimla is Rs Y then
represent the above situation algebraically.
(2) Find the cost of one ticket from Gurgaon to Chandigarh.
(3) If Raj purchases 3 tickets to Chandigarh and 5 tickets to Shimla, how much amount he will play?
OR If Anuj spends Rs 5600 to buy tickets find the total number of tickets he purchased?
Case study -11
Sumedh is a science Graduate. Driving in his passion. After finishing his Graduation he drives a taxi in
Sikkim. He charges a fixed amount together with the charge for the distance covered. A person paid him
Rs 1100 for travelling 50 Km by his taxi. On the next day a person paid him Rs 1900 for travelling 90 Km by
his taxi. Let fix charge be Rs x and additional charge Rs y per km,
Based on the given information answer the following question:
(1) What are the fixed charges for his taxi?
(2) What is the rate per km for travelling by his taxi?
(3) If in peak tourist season Sumedh increases the fixed charges by 60%, what will be the cost of
travelling 50 km by his taxi?
OR If in lean tourist season he decreases the fixed charges by 50%, what will be the cost of travelling 60
km by his taxi?

Case study-12
Mr. R.K Agarwal is owned a famous amusement park in Delhi. Generally, he does not go to park and it is
managed by team of staff. The ticket charge for the park is Rs 150 for children and Rs 400 for adults.
One day Mr Agrawal decided to random check the park and went there. When he checked the cash counter,
he found that 480 tickets were sold and Rs.134500 was collected.
Based on the above information, answer the following:-
i) Let the number of children visited he x and the number of adults visited be y. What is the correct
system of pair of linear equation?
ii) How many children are visited?
iii) How many adults are visited?
OR How much amount will be collected if 300 children and 350 adults visited the park on a particular day?
Case study -13
The residents of a group housing society at Dwarka decided to build a rectangular garden. To beautify the
garden, one of the members of the society made some calculations and informed that if the length of the
rectangular garden is increased by 2 m and the breadth reduced by 2 m, the area gets reduced by 12 sq. m. If,
however, the length is decreased by 1 m and breadth increased by 3 m, the area of the rectangle is increased
by 21 sq. m.
Let the length of rectangular plot x m. And breadth is y m.
Based on the above information Answer the following -
i) What is the linear equation for first condition.
ii) What is the linear equation for second condition.
iii) What is the length and breadth of the rectangular garden?
Or If cost of cutting the grass of the garden is Rs 400 per sq.m, Find the total cost to clean the garden.

Case study -14

Jodhpur is the second-largest city in the Indian state of Rajasthan and officially the second metropolitan
city of the state. Jodhpur was historically the capital of the Kingdom of Marwar, which is now part of
Rajasthan. Jodhpur is a popular tourist destination, featuring many palaces, forts, and temples, set in
the stark landscape of the Thar Desert. It is popularly known as the “Blue City” among people of
Rajasthan and all over India. The old city circles the Mehrangarh Fort and is bounded by a wall with
several gates. The city has expanded greatly outside the wall, though, over the past several decades.
Jodhpur is also known for the rare breed of horses known as Marwari or Malani, which are only found
here. Last year we visited Jodhpur in a group of 25 friends. When we went Mehrangarh fort we
found given fare for ride : Ride Normal Hours Fare Peak Hours Fare
Some people choose to ride on horse and rest
Horse Rs 50 3 Times
choose to ride on elephant.
Elephant Rs 100 2 Times
First day we rode in normal hours and we paid
Rs.1950 for ride, Let x be the number of horses hired and y be the number elephants hired
Based on the above information Answer the following -
i) What is the linear equation for first condition.
ii) What is the linear equation for second condition.
iii) How many horses and elephant were hired?
Or Next day we rode in peak hours, then how much total fare was paid by our group?
Case study -15
Wilton Norman “Wilt” Chamberlain was an American basketball player, and played in the NBA during
the 1960s. At 7 feet 1 inch, he was the tallest and heaviest player in the league for most of his career,
and he was one of the most famous people in the game for many years. He is the first and only
basketball player to score 100 points in an NBA game.
In the 1961–1962 NBA basketball season, Wilt Chamberlain of the Philadelphia Warriors made 30
baskets. Some of the baskets were free throws (worth 1 point each) and some were field goals (worth
2 points each). The number of field goals was 10 more than the number of free throws. Let x be the
free throw and y be the field goals.
Based on the above information Answer the following –
i) How many field goals did he make?
ii) How many free throws did he make?
iii) What was the total number of points scored?
Or If Wilt Chamberlain played 5 games during this season, what was the average number of
points per game?
ANSWERS:
1. i) 3x+2y = 80. Ii) 2x+3y = 70 III) X= 20 Rs, Y=10 Rs. Or. 120 Rs
2. I) x+10y = 800 ii) x+15y = 950. III) X= 500 Rs , Y= 30 Rs/km or 1150 Rs.

3. I) 2x+3y = 46 ii) 3x+5y = 74. III) X= 8 Rs, Y= 10 Rs. Or. 72 Rs

4. i) x+25y = 4500 ii) x+30y = 5200 iii) y= 140 Rs , x = 1000 Rs Or 3800 Rs
5. I) x – y =10 ii) x + y =70 iii) x = 40 km/hr, y= 30 km/hr or 1 hr
6. I) point (5,5) ii) 4x + 10 y = 10 ( many more answer are possible)
iii) Right angled triangle Or Area = 10 sq unit
7. I) x + y = 500 ii) x + 2y = 700 iii) x= 300 bird or Total animal =500
8. I) 60/x + 240/y = 4 ii) 100/x + 200/y =25/6 iii) 80 km per hr or 4hr
9. I) x + 50y = 10000 ii) x + 25y = 7500 iii) x = Rs.5000 or y = Rs.100per person
10. I) 2x + 3y = 3700, 3x + 4y = 5100 ii) X = 500 Rs iii) 6000Rs or Total ticket = 8
11. I) X = 100 Rs ii) Y= 20 Rs per km iii) 1160 Rs or 1250 Rs
12. I) x + y = 480 , 3x + 8y = 2690 ii) x= 230 iii) y= 250 or 185000 Rs
13. I) x – y =4, ii) 3x – y = 24 iii) L= 10m. B=6m. or Rs 24000
14. I) x + y = 25 ii) X + 2y = 39 iii) X= 11 (horse), Y= 14 ( elephant) OR Rs 4450
15. I) Y = 20 II) X = 10 III) 50 OR average= 50/5=10