Class 9th Maths - Linear Equations in Two Variables Case Study Questions and Answers 2022 - 2023
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Linear Equations in Two Variables Case Study Questions With Answer Key
9th Standard CBSE
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Reg.No. :
Mathematics
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In the below given layout, the design and measurements has been made such that area of two bedrooms and Kitchen together is 95 sq. m.
(i) The area of two bedrooms and kitchen are respectively equal to(a) 5x, 5y (b) 10x, 5y (c) 5x, 10y (c) x, y (ii) Find the length of the outer boundary of the layout.
(a) 27 m (b) 15 m (c) 50 m (d) 54 m (iii) The pair of linear equation in two variables formed from the statements are
(a) x + y = 13, x + y = 9
(b) 2x + y = 13, x + y = 9
(c) x + y = 13, 2x + y = 9
(d) None of the above
(iv) Which is the solution satisfying both the equations formed in (iii)?(a) x = 7, y = 6 (b) x = 8, y = 5 (c) x = 6, y = 7 (d) x = 5, y = 8 (v) Find the area of each bedroom.
(a) 30 sq. m (b) 35 sq. m (c) 65 sq. m (d) 42 sq. m -
Deepak bought 3 notebooks and 2 pens for Rs. 80. His friend Ram said that price of each notebook could be Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs.5 and each pen could be for Rs. 2.50. Another friend Ajay felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of each notebook would also be Rs.16.
Lohith also bought the same types of notebooks and pens as Aditya. He paid 110 for 4 notebooks and 3 pens. Later, Deepak guess the cost of one pen is Rs. 10 and Lohith guess the cost of one notebook is Rs. 30.
(i) Form the pair of linear equations in two variables from this situation by taking cost of one notebook as Rs. x and cost of one pen as Rs. y.
(a) 3x + 2y = 80 and 4x + 3y = 110
(b) 2x + 3y = 80 and 3x + 4y = 110
(c) x + y = 80 and x + y = 110
(d) 3x + 2y = 110 and 4x + 3y = 80
(ii) Which is the solution satisfying both the equations formed in (i)?(a) x = 10, y = 20 (b) x = 20, y = 10 (c) x = 15, y = 15 (d) none of these (iii) Find the cost of one pen?
(a) Rs. 20 (b) Rs. 10 (c) Rs. 5 (d) Rs. 15 (iv) Find the total cost if they will purchase the same type of 15 notebooks and 12 pens.
(a) Rs. 400 (b) Rs. 350 (c) Rs. 450 (d) Rs. 420 (v) Find whose estimation is correct in the given statement.
(a) Deepak (b) Lohith (c) Ram (d) Ajay -
Prime Minister's National Relief Fund (also called PMNRF in short) is the fund raised to provide support for people affected by natural and man-made disasters. Natural disasters that are covered under this include flood, cyclone, earthquake etc. Man-made disasters that are included are major accidents, acid attacks, riots, etc.
Two friends Sita and Gita, together contributed Rs. 200 towards Prime Minister's Relief Fund. Answer the following :
(a) Which out of the following is not the linear equation in two variables ?(i) 2x = 3 (iii) x2 + x = 1 (ii) 4 = 5x – 4y (iv) x – √2y = 3 (b) How to represent the above situation in linear equations in two variables ?
(i) 2x + y = 200 (ii) x + y = 200 (iii) 200x = y (iv) 200 + x = y (c) If Sita contributed Rs. 76, then how much was contributed by Gita ?
(i) Rs. 120 (ii) Rs. 123 (iii) Rs. 124 (iv) Rs. 125 (d) If both contributed equally, then how much is contributed by each?
(i) Rs. 50, Rs. 150 (ii) Rs. 100, Rs. 100 (iii) Rs. 50, Rs. 50 (iv) Rs. 120, Rs. 120 (e) Which is the standard form of linear equations x = – 5 ?
(i) x + 5 = 0 (ii) 1.x – 5 = 0 (iii) 1.x + 0.y + 5 = 0 (iv) 1.x + 0.y = 5 -
Sanjay bought 5 notebooks and 2 pens for Rs. 120. He told to guess the cost of each notebook and pen to his friends Mohan and Anil. Sanjay has given the clue that both the costs are positive integers and divisible by 5 such that the cost of a notebook is greater than that of a pen.
Now, Mohan and Anil tried to guess.
Mohan said that price of each notebook could be Rs. 18. Then five notebooks would cost Rs.90, the two pens would cost Rs.30 and each pen could be for Rs. 15. Anil felt that Rs. 18 for one notebook was too little. It should be at least Rs. 20. Then the price of each pen would also be Rs.10.
(i) Form the linear equations in two variables from this situation by taking cost of one notebook as Rs. x and cost of one pen as Rs. y.(a) 2x + 5y = 120 (b) 5x + y = 120 (c) x + y = 120 (d) 5x + 2y = 120 (ii) Which is the solution of the equations formed in (i)?
(a) x = 10, y = 20 (b) x = 20, y = 10 (c) x = 15, y = 15 (d) none of these (c) If the cost of one notebook is Rs. 15 and cost of one pen is 10, then find the total amount.
(i) Rs. 120 (ii) Rs. 95 (iii) Rs. 105 (iv) Rs. 125 (d) If the cost of one notebook is twice the cost of one pen, then find the cost of one pen?
(a) Rs. 20 (b) Rs. 10 (c) Rs. 5 (d) Rs. 15 (e) Which is the standard form of linear equations y = 4 ?
(i) y – 4 = 0 (ii) 1.y + 4 = 0 (iii) 0.x + 1.y + 4 = 0 (iv) 0.x + 1.y – 4 = 0 -
On his birthday, Manoj planned that this time he celebrates his birthday in a small orphanage centre. He bought apples to give to children and adults working there. Manoj donated 2 apples to each children and 3 apples to each adult working there along with birthday cake. He distributed 60 total apples.
(a) How to represent the above situation in linear equations in two variables by taking the number of children as 'x' and the number of adults as 'y'?(i) 2x + y = 60 (iii) 2x + 3y =60 (ii) 3x + 2y = 60 (iv) 3x + y =60 (b) If the number of children is 15, then find the number of adults?
(i) 10 (iii) 15 (ii) 25 (iv) 20 (c) If the number of adults is 12, then find the number of children?
(i) 12 (iii) 15 (ii) 14 (iv) 18 (d) Find the value of b, if x = 5, y = 0 is a solution of the equation 3x + 5y = b.
(i) 12 (iii) 15 (ii) 14 (iv) 18 (e) Which is the standard form of linear equations in two variables: y - x = 5?
(i) 1.y - 1.x - 5 = 0 (ii) 1.x - 1.y + 5 = 0 (iii) 1.x + 0.y + 5 = 0 (iv) 1.x - 1.y -5 = 0 -
Aditya purchased two types of chocolates A and B at the rate of Rs. x and Rs. y respectively. The total amount spent is Rs. 7. After reaching home, he forms a linear equation in two variables for two types of chocolates. He prepares a table and a graph of the linear equation as shown in adjoining graph:
(a) How a represent the above situation in linear equations in two variables?(i) 2x + y = 7 (iii) x + y = 7 (ii) x = 7 (iv) y = 7 (b) If the cost of chocolates A is 5, then find the cost of chocolates B?
(i) 3 (iii) 1 (ii) 5 (iv) 2 (c) Which of the follwing point lies on the line x + y = 7?
(i) (3, 4) (iii) (1, 5) (ii) (5, 4) (iv) (2, 6) (d) The point where the line x + y = 7 intersect y-axis is
(i) (0, 4) (iii) (7, 0) (ii) (0, 6) (iv) (0, 7) (e) For what value of k, x = 2 and y = -1 is a soluation of x + 3y -k = 0.
(i) 1 (iii) -1 (ii) -2 (iv) 2
Case Study
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Answers
Linear Equations in Two Variables Case Study Questions With Answer Key Answer Keys
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(i) (b) 10x, 5y
Area of one bedroom = 5x sq.m
Area of two bedrooms = 10x sq.m
Area of kitchen = 5y sq. m
(ii) (d) 54 m
Length of outer boundary = 12 + 15 + 12 + 15 = 54 m
(iii) (d) None of the above
Area of two bedrooms = 10x sq.m
Area of kitchen = 5y sq. m
So, 10x + 5y = 95  2x + y = 19
Also, x + 2 + y = 15 x + y = 13
(iv) (c) x = 6, y = 7
x + y = 6 + 7 = 13
2x + y = 2(6) + 7 = 19
x = 6, y = 7
x + y = 6 + 7 = 13
2x + y = 2(6) + 7 = 19
x = 6, y = 7
(v) (a) 30 sq. m
Area of living room = (15 x 7) – 30
= 105 – 30 =75 sq. m -
(i) (a) 3x + 2y = 80 and 4x + 3y = 110
Here, the cost of one notebook be Rs. x and that of pen be Rs. y.
According to the statement, we have
3x + 2y = 80 and
4x + 3y = 110
(ii) (b) x = 20, y = 10
3x + 2y = 3(20) + 2(10) = 60 + 20 = 80
4x + 3y = 4(20) + 3(10) = 80 + 30 = 110
(b) x = 20, y = 10
(iii) (b) Rs. 10
Cost of 1 pen = Rs. 10
(b) Rs. 10
(iv) (d) Rs. 420
Total cost = Rs. 15 x 20 + Rs. 12 x 10
= 300 + 120
= Rs. 420
(v) (a) Deepak
Ram said that price of each notebook could be Rs. 25.
Ajay felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16
Deepak guess the cost of one pen is Rs. 10 and
Lohith guess the cost of one notebook is Rs. 30
Therefore, estimation of Deepak is correct -
(a) (iii) x2 + x = 1
(b) (ii) x + y = 200
Here, x represents Sita's contribution and y represents Gita's contribution.
(c) (iii) Rs. 124
If x = 76 then 76 + y = 200
y = 200 - 76
y = 124
(d) (ii) Rs. 100, Rs. 100
If x = y then x + x = 200
2x = 200
x = 200/2 = 100
(e) (iii) 1.x + 0.y + 5 = 0
Since, x = -5 ⇒ x + 5 = 0
Thus, standard form of x = -5 is 1.x + 0.y + 5 = 0. -
(i) (d) 5x + 2y = 120
Here, the cost of one notebook be Rs. x and that of pen be Rs. y.
According to the statement, we have 5x + 2y = 120
(ii) (b) x = 20, y = 10
5x + 2y = 5(10) + 2(20) = 50 + 40 = 90 ≠ 120
5x + 2y = 5(20) + 2(10) = 100 + 20 = 120
5x + 2y = 5(15) + 2(15) = 75 + 30 = 105 ≠ 120
(c) (ii) Rs. 95
5x + 2y = 5(15) + 2(10) = 75 + 20 = 95
(d) (b) Rs. 10
Here, x = 2y
5(2y) + 2y
= 10y + 2y = 12y = 120
⇒ y = 10
(e) (iv) 0.x + 1.y – 4 = 0
Since, y = 4 ⇒ y – 4 = 0
Thus, standard form of y = 4 is 0.x + 1.y – 4 = 0 -
(a) (iii) 2x + 3y = 60
Let the number of children be x and the number of adults be y then the linear equation in two variable for the given situation is
2x + 3y = 60.
(b) (i) 10
2x + 3y =60 ⇒ 2(15) + 3y = 60
⇒ 3y = 60 - 30 = 30
⇒ y = 10
(c) (i) 12
2x + 3y = 60 ⇒ 2x + 3(12) = 60
⇒ 2x 60 - 36 = 24
⇒ x = 12
(d) (iii) 15
On putting x = 5 and y = 0 in the equation 3x + 5y = b, we have
3 x 5 + 5 x 0 = b
⇒ 15 + 0 = b
⇒ b = 15
(e) (ii) 1.x - 1.y + 5 = 0
y - x = 5 ⇒ y = x + 5
⇒ x - y + 5 = 0
⇒ 1.x - 1.y + 5 = 0 -
(a) (iii) x + y = 7
(b) (iv) 2
x + y = 7 ⇒ 5 + y = 7
⇒ y = 7 - 5 = 2
(c) (i) (3, 4)
(d) (iv) (0, 7)
(e) (iii) -1
On putting x = 2 and y = -1 in the equation x + 3y - k = 0, we have
2 + 3(-1) - k = 0
⇒ 2 - 3 = k
⇒ k = -1
