Please refer to MCQ Questions Chapter 3 Linear Equations Class 10 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 10 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 10 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 3 Linear Equations in Class 10 Mathematics provided below to get more marks in exams.

**Chapter 3 Linear Equations MCQ Questions**

Please refer to the following **Chapter 3 Linear Equations MCQ Questions Class 10 Mathematics** with solutions for all important topics in the chapter.

**MCQ Questions Answers for Chapter 3 Linear Equations Class 10 Mathematics**

**Question. A mother said to her son, “the sum of our present ages is twice my age 12 years ago and nine years hence, the sum of our ages will be thrice my age 14 years ago”. What is her son’s present age ? (in years) **

(a) 8

(b) 12

(c) 15

(d) 10

**Answer**

B

**Question. A told B, “when I was as old as you are now, then your age was four years less than half of my present age”. If the sum of the present ages of A and B is 61 years, what is B’s present age? (in years). **

(a) 9

(b) 25

(c) 43

(d) 36

**Answer**

B

**Question. A three digits number abc is 459 more than the sum of its digits. What is the sum of the 2 digit number ab and the 1-digit number a ? **

(a) 71

(b) 61

(c) 51

(d) Cannot be determine

**Answer**

C

**Question. The quantity of fat in a kilogram of food A plus the quantity of protein in a kilogram of food A is 100 g. The quantity of protein in a kilogram of food A minus twice the quantity of fat in a kilogram of food A is 10 g. How many grams of protein are there in akilogram of food A ? **

(a) 30

(b) 45

(c) 50

(d) 70

**Answer**

D

**Question. For what value of ‘k’ will the equations x + 2y + 7 = 0 and 2x + ky + 14 = 0 represent coincident lines ? **

(a) 2

(b) 4

(c) 6

(d) 3

**Answer**

B

**Question. Ram and Mohan are friends. Each has some money. If Ram gives Rs.30 to Mohan, then Mohan will have twice the money left with Ram. But, If Mohan gives Rs.10 to Ram, then Ram will have thrice as much as is left with Mohan. How much money does each have ? **

(a) Rs.62, Rs.34

(b) Rs.6, Rs.2

(c) Rs.170, Rs.124

(d) Rs.43, Rs.26

**Answer**

A

**Question. If(3k+1)x + 3y − 2 = 0 and (k ^{2}+1) x + (k − 2)y − 5 = 0 then the value of ‘k’ for the given equations having no solution is **

(a) 1

(b) 0

(c) − 2

(d) − 1

**Answer**

D

**Question. In a fraction if the numerator is multiplied by 3 and the denominator is reduced by 3, is equal to 18 11 , but if the numerator is increased by 8 and the de- nominator is doubled then it is equal to 2 5 . So the fraction is **

(a) 12/ 25

(b) 13/ 12

(c) 8/ 5

(d) 7/ 19

**Answer**

A

**Question. The length of the sides of a triangle are 3x + 2y, 4x + 4/3 y and 3(x + 1) + 3/ 2 (y − 1). If the triangle is equilateral, then its side is **

(a) 8

(b) 10

(c) 12

(d) 16

**Answer**

C

**Question. The solution of the equations : x/4= y/3= z/2 , 7x + 8y + 5z = 62 is : **

(a) (4,3,2)

(b) (2,3,4)

(c) (3,4,2)

(d) (4,2,3)

**Answer**

A

**Question. How can the relationship between x and y be best defined, if values of x and y are as follows ?**

**x 2 3 4 5 6**** y 0 2 6 12 20 **

(a) y = 2x − 4

(b) y = x^{2} − 3x + 2

(c) y = x^{2} − 4x

(d) y = x^{2 }− 4

**Answer**

B

**Question. If (p,p) is the solution of system of equations ax + by + (t s) = 0 and bx + ay + (s r) = 0, (a ¹ b), then which of the following must be true ? **

(a) 2r = s + t

(b) 2t = r + s

(c) 2s = r + t

(d) r + s + t = 0

**Answer**

C

**Question. 2 men and 3 boys together can do a piece of work in 8 days. The same work is done in 6 days by 3 men and 2 boys together. How long would 1 boy alone and 1 man alone take to complete the work independently. **

(a) 40 days, 120 days

(b) 120 days, 40 days

(c) 20 days, 120 days

(d) 120 days, 20 days

**Answer**

D

**Question. If 2x + 3y = 7 and (p + q) x + 2 (p − q) y = 21, then the values of p and q are (given that the system has infinite solutions). **

(a) p = 10, q = 3

(b) p = 5, q = 2

(c) p = 21 /4 , q = 3/ 4

(d) p = 10, q = 2

**Answer**

C

**Question. A sailor goes 12 km downstream in 2 hours and return to the starting point in 3 hours. Find the speed of the sailor in still water and the speed of the current. **

(a) 5 km/hr, 1 km/hr

(b) 1 km/hr, 5 km/hr

(c) 4 km/hr, 1 km/hr

(d) 3 km/hr, 1 km/hr

**Answer**

A

**Question. A half-ticket issued by railway costs half the full fare but the reservation charge is the same on half ticket as on full-ticket. One full reserved first class ticket for a journey between two stations costs Rs. 362 and one full and one half reserved first class ticket costs Rs. 554. The reservation charge is. **

(a) Rs.18

(b) Rs.22

(c) Rs.38

(d) None

**Answer**

B

**Question. Dheeraj has twice as many sisters as he has brothers. If Deepa, Dheerajs sister has the same number of brothers as she has sisters, then Deepa has how many brothers ? **

(a) 2

(b) 3

(c) 4

(d) Cannot be determined

**Answer**

B

**Question. There are two examination rooms A and B. If 10 candiates are sent from room A to room B, the number of candiates in each room is the same, while if 20 are sent from room B to room A, the number in room A becomes double the number in room B. The number of candidates in each room are respectively **

(a) 80 and 100

(b) 100 and 80

(c) 80 and 120

(d) 100 and 60

**Answer**

B

**Question. Swati starts her job with certain monthly salary and earns a fixed increment every year. If her salary was Rs. 22500 per month after 6 years of service and Rs.30000 per month after 11 years of service. find her salary after 8 years of service (in Rs.). **

(a) 24000

(b) 25500

(c) 26000

(d) 24500

**Answer**

B

**Question. 5 pens and 6 pencils together cost Rs. 9 and 3 pens and 2 pencils cost Rs. 5. Find the cost of 1 pen and 1 pencil. **

(a) Rs. 2, Rs. 0.50

(b) Rs.1.50, Rs.0.25

(c) Rs.1.50, Rs.0.50

(d) Rs.2, Rs.0.25

**Answer**

B

**Question. If the demand for fertilizer product is given by p + 5q = 21 and the supply is determined by p 2q = 7, where p and q denote the price of the commodity and q is the number of units of fertilizer product supplied. If a man wants to buy q units of fertilizer product, then the amount paid by him is **

(a) Rs.22

(b) Rs.30

(c) Rs.32

(d) Rs.24

**Answer**

A

**Question. Consider the system of linear equations ****2x + 3y + 4z = 16****4x + 4y + 5z = 26****ax + by + cz = r****For r = 5 and a = 1 the system of linear equation will have infinite number of solutions, if c =**

(a) 3/2

(b) 1

(c) 1/2

(d) 0

**Answer**

C

**Question. A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Sanchit paid Rs.45 for a book kept for 7 days, while Karan paid Rs.25 for the book he kept for 5 days. The fixed charge and the charge for each extra day is **

(a) Rs.5 and Rs.10

(b) Rs.10 and Rs.5

(c) Rs.15 and Rs.5

(d) Rs.5 and Rs.15

**Answer**

A

**Question. If 173x + 197y = 149 and 197x + 173y = 221 then find (x,y). **

(a) (3, − 2)

(b) (2,1)

(c) (1, − 2)

(d) (2,−1)

**Answer**

D

**Question. If 2x + 3y = 78 and 3x + 2y = 72, what is the value of x + y ? **

(a) 36

(b) 32

(c) 30

(d) Cannot be determined

**Answer**

C

**Question. Mallesh has some cows and some hens in his shed. The total number of legs is 92 and the total number of heads is 29. Find the number of cows in his shed. **

(a) 12

(b) 14

(c) 17

(d) 19

**Answer**

C

**Question. In a examination, a student attempted 15 questions correctly and secured 40 marks. If there were two types of questions (2 marks and 4 marks question), how many questions of 2 marks did he attempt correctly ? **

(a) 5

(b) 10

(c) 20

(d) 40

**Answer**

B

**Question. If 3Y + 9X = 54 and 28X/13Y = 140/39 then what is the value of Y − X ? **

(a) −1

(b) −2

(c) 2

(d) 1

**Answer**

B

**Question. In a zoo, there are rabbits and pigeons. If their heads are counted, there are 90 while their legs are 224. Find the number of pigeons in the zoo. **

(a) 70

(b) 68

(c) 72

(d) 22

**Answer**

B

**Question. A test has 50 questions. A student scores 1 mark for a correct answer, − 1/3 for a wrong answer and − 1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than **

(a) 6

(b) 12

(c) 3

(d) 9

**Answer**

C

**Question. At the first stop on his route, a driver unloaded 2/5 of the packages in his van. After be unloaded another three pakages at his next stop, 1/2 of the original number of packages remained. How many packages were in the van before the first delivery ? **

(a) 25

(b) 10

(c) 30

(d) 36

**Answer**

C

**Question. The pair of equations 3x+y = 81 ; 81 ^{x−y} = 3 has **

(a) no solution

(b) the solution x= 2,1/2,y= 1,7/8

(c) the solution x = 2, y = 2

(d) the solution x = 2 ,1/8,y=1, 8/7

**Answer**

D

**Question. Find the value of x and y, if 5x/8 + 7y /18 = 6 and 2(x − y) = −10. **

(a) 4,9

(b) 5,7

(c) 3,12

(d) 10,4

**Answer**

A

**Question. If the numerator and the denominator of a fraction are each increased by 4, the fraction becomes 2 and when numerator and denominator of the same fraction are each decreased by 6, the fraction becomes 12. The sum of the numerator and the denominator is **

(a) 11

(b) −11

(c) 25

(d) −25

**Answer**

C

**Question. The equations 3x − 4y = 5 and 12x − 16y = 20 have **

(a) No common solution

(b) Exactly one common solution

(c) Exactly two common solutions

(d) More than two common solutions

**Answer**

D

**Question. Shyam had 85 currency notes in all, some of which were of Rs.100 denomination and the remaining of Rs.50 denomination. The total amount of all these currency notes was Rs.5000. How much amount in rupees did he have in the denomination of Rs.50 ? **

(a) 3500

(b) 70

(c) 15

(d) 1500

**Answer**

A

**Question. There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Rs.42 per day while the average expenditure per head iminished by Rs 1. Find the original expenditure of the mess. **

(a) Rs.480

(b) Rs.520

(c) Rs.420

(d) Rs.460

**Answer**

C

**Question. In a ΔABC, ÐA = x°, ÐB = y° and ÐC = (y + 20)°. If 4x − y = 10, then the triangle is **

(a) right angled

(b) obstuse angled

(c) equilateral

(d) None of these

**Answer**

A

**Question. A florist was asked to make a bouquet with exactly Rs.1000 with 100 sticks of roses of three colours- Pink, Yellow and Red. While Pink roses cost Rs. 0.50 per stick, Red roses cost Rs.10.00 per stick and Yellow roses cost Rs. 50.00 per stick. How many Red roses did the florist use in the bouquet ? **

(a) 1

(b) 5

(c) 80

(d) Several combinations are possible

**Answer**

A

**Question. A student was asked to divide a number by 17/8. Instead, he actually multiplied it by 17/8 and hence got 225 more than the expected answer. What was the expected answer ? **

(a) 126

(b) 136

(c) 64

(d) None of these

**Answer**

B

**Question. In an examination there are 30 questions. 1 mark is given for each correct answer and 0.25 is deducted for every incorrect answer. Ankur attempted all the questions and scored 13.75. How many incorrect answers did he have ? **

(a) 10

(b) 11

(c) 12

(d) None of these

**Answer**

D

**Question. Which one of the following conditions must a, b and c satisfy so that the following system of linear simultaneous equations has at least one solution, such that a + b + c ≠ 0****m + 2n − 3r = a****2m + 6n − 11 r = b****m − 2n + 7r = c **

(a) 5a + 2b + c = 0

(b) 5a + 2b − c = 0

(c) 5a − 2b − c = 0

(d) 5a − 2b + c = 0

**Answer**

C

**Question. A woman sells to the first customer half her stock and half an apple, to the second customer she sells half her remaining stock and half an apple, and so on to the third, and to a fourth customer. She finds that she has now 15 apples left. How many apples did she have before she started selling ? **

(a) 63

(b) 127

(c) 240

(d) None of these

**Answer**

D

**Question. To a proper fraction, when six is added to the numerator and the denominator is increased by its 50%, the ratio becomes 1/ 2 and when the numerator is multiplied by 4 and denominator is reduced by 8, then the fraction becomes 3. The fraction (simplified) is **

(a) 1/ 3

(b) 15/ 28

(c) 33/ 52

(d) Cannot be determined

**Answer**

D

**Question. The sum of the two digits of a number is 15. If 9 be added to the number, then the digits are re- versed. The number is**

(a) 96

(b) 87

(c) 78

(d) 69

**Answer**

C

**Question. If 2/x + 3/y = 13 and 5/x – 4/y –2, then the values of x and y respectively are **

(a) 1/ 2 , 1/ 3

(b) 1/ 3 , 1/ 4

(c) 1/ 2 , 1/ 5

(d) 2, 3

**Answer**

A

**Question. If 7x − 2y/xy = 5 and 8x + 7y/xy = 15 , then **

(a) x = 1 , y = 1

(b) x = 2, y = 2

(c) x = 3 , y = 4

(d) x = 2, y = 1

**Answer**

A

**Question. If 1/ x = u and 1/ y = v, then 2/x + 3/y = 13 becomes **

(a) 3u + 2v = 13

(b) 2u + 3v = 13

(c) 2/u + 3/v = 13

(d) 2/v + 3/u = 13

**Answer**

B

**Question. A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, the number of hens will be **

(a) 18

(b) 26

(c) 32

(d) 40

**Answer**

B

**Question. A motor boat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. The speed of the stream is **

(a) 60 km/hr

(b) 6 km/min

(c) 6 km/s

(d) 6 km/hr

**Answer**

D

**Question. Equation 5/x-1 + 1/y-2 = 2 is reduced in linear equation as 5p + q = 2. Then the values of p and q respectively are **

(a) 1/x-1 , 1/y-2

(b) 1/y-1 , 1/x-2

(c) x – 1, y – 2

(d) x + 1, y + 2

**Answer**

A

**Question. A part of monthly Hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess.When Swati takes food for 20 days, she has to pay 3000 as hostel charges whereas, Mansi who takes food for 25 days pays ` 3500 as hostel charges. The fixed charges and the cost of food per day, respectively are **

(a) `400, `300

(b) `300, `200

(c) `1000, `100

(d) `500, `100

**Answer**

C

**Question. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, (in years) of the son and the father are, respectively **

(a) 4 and 24

(b) 5 and 30

(c) 6 and 36

(d) 3 and 24

**Answer**

C

**Question. Children were fallen in for drill. If each row contained 4 children less, 10 more rows would have been made. But if 5 more children were fallen in each row, the number of rows would have reduced by 5. The number of children in the school is **

(a) 150

(b) 160

(c) 170

(d) 120

**Answer**

C

**Question. A fraction becomes 3 1 when 2 is subtracted from the numerator and it becomes 2 1 when 1 is subtracted from the denominator. The fraction is **

(a) 2 5

(b) 5 18

(c) 4 13

(d) 7 15

**Answer**

D

**Question. Meena went to a bank to withdraw ` 2,000. She asked the cashier to give her ` 50 and ` 100 notes only. Meena got 25 notes in all. How many notes of ` 50 and ` 100 she received? **

(a) `50 : 10, `100 : 15

(b) `50 : 12, `100 : 10

(c) `50 : 15, `100 : 10

(d) None of these

**Answer**

A

**Question. Jamila sold a table and a chair for ` 1050, thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair, she would have got ` 1065. Then the cost price of each is **

(a) Table : `500, chair : `400

(b) Table : `400, chair : `500

(c) Table : `700, chair : `600

(d) None of these

**Answer**

A

**Question. A two-digit number is obtained by either multiplying the sum of digits by 8 and then subtracting 5 or by multiplying the difference of digits by 16 and adding 3. The number is **

(a) 23

(b) 34

(c) 83

(d) 119

**Answer**

C

**Question. When does the pair of linear equations 7x + ky = k;14x + 2y = k +1 have infinitely many solutions? **

(a) k = 1

(b) k ≠1

(c) k = 2

(d) k = 4

**Answer**

A

**Question. The pair of linear equations x + y = 3; 2x + 5y = 12 has a unique solution x = x1 , y = y1 Find the value of x1 . **

(a) 1

(b) 2

(c) -1

(d) -2

**Answer**

A

**Question. Which of the following solutions does the pair of linear equations x + 2y = 5 ; 3x +12y = 10 have? **

(a) A unique solution

(b) No solution

(c) More than two solutions

(d) Infinitely many solutions

**Answer**

A

**Question. Find the number of solutions of the equations x +1/y = 2 and 2xy – 3y = -2 . **

(a) 0

(b) 1

(c) 2

(d) Infinitely many

**Answer**

A

**Question. If the equations 4x + 7y = 10 and 10x + ky = 25 represent coincident lines, what is the value of ‘k’? **

(a) 5

(b) 17/2

(c) 27/2

(d) 35/2

**Answer**

D

**Question. What is the condition that a system of simultaneous equations a _{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 must satisfy to have exactly one solution? **

(a) a

_{1}/a

_{2}= b

_{1}/b

_{2}

(b) a

_{1}/a

_{2}≠ b

_{1}/b

_{2}

(c) a

_{1}/a

_{2}= c

_{1}/c

_{2}

(d) b

_{1}/b

_{2}= c

_{1}/c

_{2}

**Answer**

B

**Question. cm Find ‘x’ and ‘y’ for the equations x/3 + y/4 = 4 and 5x /3 + y/4 = 8 . **

(a) x = 8,y = 6

(b) x = 3,y = 4

(c) x = 6,y = 8

(d) x = 4,y – 6

**Answer**

C

**Question. For what value of ‘k’, will the equations 4x + 6y =11 and 2x + ky = 7 be inconsistent? **

(a) 2

(b) 3

(c) 4

(d) 8

**Answer**

B

**Question. ₹ 49 was divided among 150 children. Each girl got 50 paise and a boy 25 paise. How many boys were there? **

(a) 100

(b) 102

(c) 104

(d) 105

**Answer**

C

**Question. The area of a rectangle increases by 76 square units, if the length and breadth are each increased by 2 units. However, if the length is increased by 3 units and breadth is decreased by 3 units, the area gets reduced by 21 square units. Find the sum of the length and breadth of the rectangle. **

(a) 40 units

(b) 42 units

(c) 4 units

(d) 36 units

**Answer**

D

**Question. What number must be added to each of the numbers, 5, 9, 17, 27 to make them proportionate? **

(a) 2

(b) 1

(c) 3

(d) 5

**Answer**

C

**Question. The solution of 2x + 3y = 2 and 3x + 2y = 2 can be represented by a point. In which of the following parts of the coordinate plane does the point lie? **

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

**Answer**

A

**Question. Which of the following is a linear equation? **

(a) x – 2y = 7

(b) x^{3} -1= 0

(c) x + 6/x = 12

(d) x/2 + 3/x = 14

**Answer**

A

**Question. If 3a/x − 2b / y + 5 = 0 and a/ x 3b/ y – 2 = 0, then **

(a) x = 1/ a , y = 1/ b

(b) x = 1/ b , y = 1/ a

(c) x – a, y = b

(d) x = a, y = –b

**Answer**

C

**Question. If 57/x + y + 6/x −y = 5 and 38/x+y + 21/x−y = 9 , then **

(a) x = 5 , y = 3

(b) x = 11, y = 8

(c) x = 9 , y = –9

(d) x = 3, y = 4

**Answer**

B

**One Word Questions :**

**Question. At what point does the line 5x + 3y = 15 intersects the x-axis?**

**Answer**

(3, 0)

**Question. If speed of a boat in still water is 25km/hr and speed of stream is 5km/hr, what are the speeds of boat in upstream and downstream?**

**Answer**

20km/hr, 30km/hr

**Question. What type of lines are these : 2x + 3y – 1 = 0, 6x + 9y + 10 = 0?**

**Answer**

Parallel

**Question. A man has only 50 paisa coins and 25 paisa coins in his purse. If the ratio of coins is 4 : 5 and amount Rs 13 in all, how many coins of each does he have?**

**Answer**

50 paisa coins = 16 , 25 paise coins = 20

**Question. What is the y coordinate of the point which lies on the line 3x + y = 5 and whose x-coordinate is 1?**

**Answer**

y = 2

**Question. What is the length of base of triangle formed the lines x – y – 1 = 0, 2x + y = 8 and yaxis in the figure below? **

**Answer**

9 units

**Question. If C and F denote the temperature of celcius and fahrenhiet scales respectively, then the following relations holds : C = 5/9 (F – 32). Find the value of C when F = 86.**

**Answer**

30

**Question. A number is as much greater than 15 as it is less then 25. Find the number.**

**Answer**

20

**Question. For what value of K the pair of linear equations has infinite solutions?****4x + y = 3****12x + 3y = 3K**

**Answer**

K = 3

**Question. A man rowing at the rate of 5km/hr in still water takes thrice as much time to going 40km up the stream as in going 40km down the stream. Find the rate at which the river flows?**

**Answer**

2 , 1/2

**Question. How many solutions the following simultaneous linear equations have?****4x + 6y = 9, 2x + 3y = –11**

**Answer**

No Solution

**Question. What are the points of intersection of the line x/a + y/b – 2 = 0 with x-axis and with y-axis?**

**Answer**

(2a, 0)(0, 2b)

**Question. Find two solutions of the equation 2x + 3y = 5.**

**Answer**

(1, 1)(4, –1)

**Question. If a system of equation is inconsistent, then what type of graph the equations will have?**

**Answer**

Parallel lines

**Question. The line 2x + 2 = x + 4 is parallel to which axis?**

**Answer**

y-axis

**Question. Give equation of a line in two variables which passes through the origin.**

**Answer**

ax + by = 0

**Question. At what point do the lines x – y = 0 and x + y = 0 intersects?**

**Answer**

origin (0, 0)

**Question. The sum and difference of ages of Reema and her elder sister are 60 years and 10 years. Find their ages.**

**Answer**

25 years, 35 years

**Question. What value of p will satisfy the equation px + 2y = 5 when x = 3, y = 1?**

**Answer**

p = 1

**Question. If ratio of three angles of a triangle is 1 : 2 : 3, what are the measures of three angles in degrees?**

**Answer**

30°, 60°, 90°

**Question. Find the value of x and y from the following simultaneous linear equations.****x + y = 7, 5x + 12y = 7**

**Answer**

x = 11, y = –4

**Question. How many variables are there in the equation 2x – 3y + 4 = 0?**

**Answer**

2

**Question. Find the increase in area of a rectangle (15m×13m ) if 7 is added to both sides of a rectangle.**

**Answer**

245m²

**Question. The point (–4, 0) lies on which axis?**

**Answer**

x-axis

**Question. Find the coordinates of two points which lie on the line x + 7y = 1.**

**Answer**

(1, 0) (8, –1)

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