Class 10 Pair of Linear Equations in Two Variables Previous Year Questions

    Q1:

    Question Image

    A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹50 and for each table is ₹200. The school spends ₹30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300. If the school rents 'x' chairs and 'y' tables, answer the following questions: (i) Write down the pair of linear equations representing the given information. (ii) (a) Find the number of chairs and number of tables rented by the school. OR (b) If the school wants to spend a maximum of ₹27,000 on 300 items (tables and chairs), then find the number of chairs and tables it can rent. (iii) What is maximum number of tables that can be rented in ₹30,000 if no chairs are rented ?

    CBSE [2025]

    Medium

    Q2:

    Assertion (A) : The pair of linear equations \(px + 3y + 59 = 0\) and \(2x + 6y + 118 = 0\) will have infinitely many solutions if \(p = 1\). Reason (R): If the pair of linear equations\( px + 3y + 19 = 0\) and \(2x + 6y + 157 = 0\) has a unique solution, then \(p ≠ 1\).

    CBSE [2025]

    Easy

    Q3:

    The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is : (A) x = -3 (B) x = 3 (C) y = -3 (D) y = 3

    CBSE [2025]

    Easy

    Q4:

    The line represented by the equation x - y = 0 is : (A) parallel to x-axis (B) parallel to y-axis (C) passing through the origin (D) passing through the point (3, 2)

    CBSE [2025]

    Easy

    Q5:

    Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received ₹1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹20 more as annual interest. How much money did he invest in each scheme ?

    CBSE [2025]

    Hard

    Q6:

    If x = 1 and y = 2 is a solution of the pair of linear equations 2x 3y + a = 0 and 2x + 3y b = 0, then : (A) a = 2b (B) 2a = b (C) a + 2b = 0 (D) 2a + b = 0

    CBSE [2025]

    Easy

    Q7:

    A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are 20 poor and 5 rich children, whereas in batch II, there are 5 poor and 25 rich children. The total monthly collection of fees from batch I is ₹9000 and from batch II is ₹26,000. Assume that each poor child pays ₹x per month each rich child pays ₹y per month. Based on the above information, answer the following questions:

    CBSE [2023]

    Medium

    Q8:

    Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.

    CBSE [2023]

    Hard

    Q9:

    The pair of equations ax + 2y = 9 and 3x + by = 18 represent parallel lines, where a, b are integers, if : (a) a = b (b) 3a = 2b (c) 2a = 3b (d) ab = 6

    CBSE [2023]

    Easy

    Q10:

    Two schools ‘P’ and ‘Q’ decided to award prizes to their students for two games of Hockey ₹x per student and Cricket ₹y per student. School ‘P’ decided to award a total of ₹9,500 for the two games to 5 and 4 students respectively; while school ‘Q’ decided to award ₹7,370 for the two games to 4 and 3 students respectively. Based on the above information, answer the following questions : (i) Represent the following information algebraically (in terms of x and y). (ii) (a) What is the prize amount for hockey ? OR (b) Prize amount on which game is more and by how much ? (iii) What will be the total prize amount if there are 2 students each from two games ?

    CBSE [2023]

    Medium

    Q11:

    The pair of linear equations 2x = 5y + 6 and 15y = 6x – 18 represents two lines which are : (a) intersecting (b) parallel (c) coincident (d) either intersecting or parallel

    CBSE [2023]

    Easy

    Q12:

    If 217x + 131y = 913 and 131x + 217y = 827, then solve the equations for the values of x and y.

    CBSE [2023]

    Medium

    Q13:

    If the system of linear equations 2x + 3y = 7 and 2ax + (a + b)y = 28 have infinite number of solutions, then find the values of' 'a' and 'b'.

    CBSE [2023]

    Easy

    Q14:

    The pair of equations x = a and y = b graphically represents lines which are: (A) parallel (B) intersecting at (b, a) (C) coincident (D) intersecting at (a, b)

    CBSE [2023]

    Easy

    Q15:

    Half of the difference between two numbers is 2. The sum of the greater number and twice the smaller number is 13. Find the numbers.

    CBSE [2023]

    Medium

    Q16:

    The value of k for which the pair of equations kx = y + 2 and 6x = 2y + 3 has infinitely many solutions is: (A) k = 3 (B) does not exist (C) k = -3 (D) k = 4

    CBSE [2023]

    Easy

    Q17:

    The hypotenuse of a right angled triangle is 6 cm more than twice the length of the shortest side. If the length of third side is 6 cm less than thrice the length of shortest side, then find the dimensions of the triangle.

    CBSE [2022]

    Medium

    Q18:

    The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two numbers becomes 260. Find the numbers.

    CBSE [2022]

    Medium

    Q19:

    The difference of the squares of two numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers.

    CBSE [2022]

    Medium

    Q20:

    A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.

    CBSE [2022]

    Medium