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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Linear Equations in Two Variables- 1 - Class 10 MCQ

Math Olympiad Test: Linear Equations in Two Variables- 1 - Free MCQ


MCQ Practice Test & Solutions: Math Olympiad Test: Linear Equations in Two Variables- 1 (10 Questions)

You can prepare effectively for Class 10 Olympiad Preparation for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Math Olympiad Test: Linear Equations in Two Variables- 1". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 1
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What are the values of x and y if

Detailed Solution: Question 1

Let

then 57a + 6b = 5 ...(1)
38a + 21b = 9 ...(2)
Solving (1) and (2) we get a = 1/19, b = 1/3
Hence
x + y = 19 ...(4)
x - y = 3 ...(5)
Solving (4) and (5), we get x = 11, y = 8

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 2
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The sum of two numbers is 16 and the sum of their reciprocals is 1/3. What are the numbers?

Detailed Solution: Question 2

Let the numbers be x and y
x + y = 16 ...(1)
and

Now


⇒ x - y = 8 ...(2)
From (1) and (2), we get x = 12, y = 4.

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Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 3
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In a triangle ΔABC, 3∠B = ∠C = 2 (∠A + ∠B). Which angle is the largest and what is its value?

Detailed Solution: Question 3

L et ∠A = x°, ∠B = y°, ∠C = 3∠B = 3y°
In ΔABC, ∠A + ∠B + ∠C = 180°
x° + y° +3y° = 180°
x° + 4y° = 180 ...(1)
∠C = 2(∠A + ∠B) ⇒ 3y = 2 (x° + y°)
2x° - y° = 0 ...(2)
From (1) and (2)
x = 20 , y = 40
∴ ∠A = 20°, ∠B = 40°, ∠C = 3 × 40 = 120°

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 4
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What is the value of k for which the system of equations 3x + y = 1 and (2k - 1) x + (k - 1) y = 2k + 1 has no solution.

Detailed Solution: Question 4

For no solution, it must have

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 5
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What are the values of x and y, if 2(ax - by) + (a + 4b) = 0 and 2 (bx + ay) + (b - 4a) = 0

Detailed Solution: Question 5

We have
2ax - 2by = - a - 4b ...(1)
and 2bx + 2ay = 4a - b ...(2)
2a2x - 2aby = -a2 - 4ab ...(3)
Now 2b2x + 2aby = 4ab - b2
2x (a2 + b2) = - (a2 + b2) ⇒ x = -1/2
Now putting the value of 2aby from eq. (3), we get

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 6
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The length of a field exceeds its breadth by 3 meters. If the length is increased by 3 meters and the breadth is decreased by 2 meters. The area remains the same. What are the length and breadth respectively of the field?

Detailed Solution: Question 6

Let the breadth of the field be x m and length be y m.
Then, area = xy m2
Now y = 3 + x
⇒ y - x = 3 ...(1)
New length = y + 3
breadth = x -2
∴ area =  (x - 2) (y + 3) = xy
⇒ xy + 3x - 2y - 6 = xy
⇒ 3x -2y = 6 ...(2)
From (1) and (2), we get
x = 12 m, y = 15 m

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 7
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What is the value of k except which the given system of equations has a unique solution?
2x + 3y - 5 = 0 and kx - 6y - 8 = 0

Detailed Solution: Question 7

The given system of equations are 
2x + 3y – 5 = 0 
kx - 6y - 8 = 0 
This system is of the form: 
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 
where, a1 = 2, b1 = 3, c1 = -5 and a2 = k, b2 = -6, c2 = -8 
Now, for the given system of equations to have a unique solution, we must have:

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 8
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Five years ago, Ravi was thrice as old as Shashi. Ten years later Ravi will be twice as old as Shashi. What is the age of Shashi?

Detailed Solution: Question 8

Let Shashi’s present age be x and Ravi’s present age be y
y - 5 = 3 (x - 5) ⇒ 3x - y = 10 ...(1)
y + 10 = 2 (x + 10) ⇒ 2x - y = 10 ...(2)
Solving eqns (1) and (2), we get
x = 20, y = 50

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 9
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In a cyclic quadrilateral ABCD, ∠A = 2x - 1, ∠B = y + 5, ∠C = 2y + 15, ∠D = 4x - 7. Which is the greatest angle of quadrilateral.

Detailed Solution: Question 9

In a cyclic quadrilateral,
∠A + ∠C = 180°, ∠B + ∠D = 180°
Here 2x - 1 + 2y + 15 = 180°
⇒ 2x + 2y = 166
x + y = 83 ...(1)
and 4x - 7 + y + 5 = 180°
⇒ 4x + y = 182 ...(2)
Solving eq. (1) and (2), we get x = 33, y = 50
∠A = 2x - 1 = 2 × 33 - 1 = 65°
∠B = y + 5 = 50 + 5 = 55°
∠C = 2y + 15 = 2 × 50 + 15 = 115°
∠D = 4x - 7 = 4 × 33 - 7 = 125°

Math Olympiad Test: Linear Equations in Two Variables- 1 - Question 10
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Rajesh scored 40 marks on a test getting 3 marks for each right answer and losing one mark for each wrong answer. If 4 marks have been awarded for each correct answer and 2 marks have been deducted for each incorrect answer then Rajesh will score 50 marks. What is the number of questions in the test?

Detailed Solution: Question 10

Let the number of right answer be x and the number of wrong answer be y
3x - y = 40 ...(1)
4x - 2y = 50 ⇒ 2x - y = 25 ...(2)
Solving (1) and (2) x = 15, y = 5
No. of questions = 15 + 5 = 20

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This test contains 10 MCQs on Math Olympiad Test: Linear Equations in Two Variables- 1 with detailed solutions for each question. It is part of the Olympiad Preparation for Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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