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CBSE Class 10  >  Class 10 Test  >  The Complete SAT Course  >  Test: Linear Equations in One Variable - 1 - Class 10 MCQ

Linear Equations in One Variable - 1 - Free MCQ Practice Test with solutions,


MCQ Practice Test & Solutions: Test: Linear Equations in One Variable - 1 (10 Questions)

You can prepare effectively for Class 10 The Complete SAT Course with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Linear Equations in One Variable - 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: 15 minutes
  • - Number of Questions: 10

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Test: Linear Equations in One Variable - 1 - Question 1
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If 50 is subtracted from two-third of a number, the result is equal to sum of 40 and one-fourth of that number. What is the number?

Detailed Solution: Question 1

Let the number be x.

According to Question,

2x/3 - 50 = x/4 + 40

⇒ 5x/12 = 90

⇒ x = (90 x 12)/5

⇒ x = 216

∴ The number is 216.

Test: Linear Equations in One Variable - 1 - Question 2
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A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?

Detailed Solution: Question 2

Given:

Number of Five rupee note = Number of Ten rupee note = Number of Twenty rupee note

Calculation:

Let the equal number of five, ten and twenty rupee notes be x

⇒ 5x + 10x + 20x = 385

⇒ 35x = 385

⇒ x = 385/35 = 11

Total number of notes = 11 notes of Rs 5 + 11 notes of Rs 10 + 11 Rs of 20 =  33 notes

Check:

11 notes of Rs 5 + 11 notes of Rs 10 + 11 Rs of 20 = 11 × 5 + 11 × 10 + 11 × 20 = 55 + 110 + 220 = Rs. 385

Total number of notes = 11 × 3 = 33 

Therefore the correct answer is 33.
Alternate Method:

Since the number of Rs 5, Rs 10, and Rs 20 notes are equal, the ratio of the number of notes is = 1 ∶ 1 ∶ 1

Or, we can say, the total number of notes must be multiple of 3.

 Only two options are multiple of 3, others can be eliminated.

option 2 : 33. That means the number of notes of each dimension is 33/3 = 11.

5 × 11 + 11 × 10 + 11 × 20 = 385

∴ The total number of notes is 33.

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Test: Linear Equations in One Variable - 1 - Question 3
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If the sum and product of two numbers is 34 and 288 respectively, find the sum of their cubes.

Detailed Solution: Question 3

Let the numbers be ‘x’ and ‘y’

Given, sum = x + y = 34

Product = xy = 288

we need to find   x3 + y3

As we know, x3 + y3 = (x + y)3 – 3xy(x + y) = (x + y)[(x + y)2 – 3xy]

put the values of x + y and xy in to the equation

∴ Sum of their cubes = 34 × [(34)2 – 3 × 288] = 34 × (1156 – 864) = 34 × 292 = 9928

Test: Linear Equations in One Variable - 1 - Question 4
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If x6 + x5 + x4 + x3 + x2 + x + 1 = 0, then find the value of x5054 + x6055 - 7

Detailed Solution: Question 4

Given:

x6 + x5 + x4 + x3 + x2 + x + 1 = 0

Calculation:

Considering the given equation

x6 + x5 + x4 + x3 + x2 + x + 1 = 0      -----(1)

In equation (1) multiplying by x

x7 + x6 + x5 + x4 + x3 + x2 + x = 0      -----(2)

Equation (2) – (1)

⇒ x7 - 1 = 0

⇒ x7 = 1

x5054 + x6055 - 7

⇒ (x7)722 + (x7)865 – 7

⇒ (1)722 + (1)865 – 7

⇒ 1 + 1 – 7

⇒ - 5

∴ Required value is – 5

Test: Linear Equations in One Variable - 1 - Question 5
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Lata makes 20 kg paneer at home and sells it every morning. From one litre of milk, she makes 200 gms of paneer. The cost of a litre of milk is Rs. 40. How much money does she spend in procuring milk every day?

Detailed Solution: Question 5

⇒ Milk used to make 200 gms of panner = 1 litre

⇒ Milk used to make 20 kgs paneer = (20 × 1000/200) × 1 = 100 litre

⇒ Cost of 1 litre milk = Rs. 40

⇒ Cost of 100 litre Milk = 100 × 40 = Rs. 4000

Test: Linear Equations in One Variable - 1 - Question 6
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In a group of 1300 students, every student reads 5 subjects and every subject is read by 65 students. The number of subjects are:

Detailed Solution: Question 6

Each of the 1300 students reads 5 subjects, so the total number of student-subject enrollments is 1300 × 5 = 6500.

Each subject is read by 65 students, so the number of different subjects equals 6500 ÷ 65 = 100

Therefore the number of subjects is exactly 100

So, Correct Option: A

Test: Linear Equations in One Variable - 1 - Question 7
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When you reverse the digits of the number 13, the number increases by 18. How many other two‐digit numbers increase by 18 when their digits are reversed?

Detailed Solution: Question 7

Calculation:

Let the unit digit be x and tens digit be y

According to the question,

⇒ 10y + x - (10x + y) = 18

⇒ 9y - 9x = 18

⇒ y - x = 2

It means that difference of digits of two-digit numbers is 2.

∴ Six cases other than (13, 31) are possible

(24, 42) (35, 53) (46, 64) (57, 75) (68, 86) (79, 97)
Mistake Points:
Here we cannot take (20, 2)
Because 2 is not a two-digit number. Normally we do not write numbers from 1 - 9  as 01, 02, 03, 04, 05, 06, 07, 08, and 09.

Test: Linear Equations in One Variable - 1 - Question 8
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The solution of equation 10x + 26 = 0 is a / an________.

Detailed Solution: Question 8

Given:

The given equation is 10x + 26 = 0

Concept:

Rational numbers are the numbers that can be written in the form of p/q, where q is not equal to zero. 

Calculation:

10x + 26 = 0

⇒ 10x = -26

⇒ x = (-26)/10

⇒ x = -13/5

∴ 10x + 26 = 0 is a rational number.

Test: Linear Equations in One Variable - 1 - Question 9
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Difference of two numbers is 50% of the smaller number. If greater number is 120, then find sum of both numbers is:

Detailed Solution: Question 9

Given:

Greater number = 120

Calculation:

Let smaller number be x

According to the question

120 – x = x × (50/100)

⇒ 120 – x = x/2

⇒ 240 – 2x = x

⇒ x + 2x = 240

⇒ 3x = 240

⇒ x = 240/3

⇒ x = 80

∴ Sum of both numbers = 120 + 80 = 200

Test: Linear Equations in One Variable - 1 - Question 10
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If x2 - 7x + 1 = 0 then find the value of (x + 1/x).

Detailed Solution: Question 10

Given:

x2 - 7x + 1 = 0

Calculation:

x2 - 7x + 1 = 0

Dividing by x:

⇒ x - 7 + 1/x = 0

⇒ x + 1/x = 7

∴ Value of x + 1/x = 7 

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About this Class 10 Practice Test

This test contains 10 MCQs on Linear Equations in One Variable - 1 with detailed solutions for each question. It is part of the The Complete SAT Course 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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