Pair of Linear Equations - Word Problems MCQ & Objective Questions
Understanding "Pair of Linear Equations - Word Problems" is crucial for students preparing for school and competitive exams. These problems not only enhance your problem-solving skills but also help in scoring better through focused practice. Engaging with MCQs and objective questions allows you to grasp key concepts and identify important questions that frequently appear in exams.
What You Will Practise Here
Formulating linear equations from word problems
Solving pairs of linear equations using substitution and elimination methods
Interpreting real-life scenarios through mathematical models
Identifying key terms and phrases that indicate relationships
Graphical representation of linear equations
Understanding the significance of solutions in context
Common applications in age problems, distance problems, and mixture problems
Exam Relevance
The topic of "Pair of Linear Equations - Word Problems" is a staple in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to set up equations based on given scenarios and solve them. Common patterns include direct word problems, multi-step problems, and questions that involve interpreting graphical data.
Common Mistakes Students Make
Misinterpreting the relationships described in the problem
Failing to convert verbal statements into mathematical equations accurately
Overlooking the need for both equations when solving
Confusing the methods of substitution and elimination
Neglecting to check the solution in the context of the problem
FAQs
Question: What is the best way to approach a word problem involving linear equations? Answer: Start by identifying the variables, then translate the problem into equations based on the relationships described.
Question: How can I improve my speed in solving these problems? Answer: Regular practice with MCQs and timed quizzes will help you become more efficient in identifying and solving problems quickly.
Question: Are there specific types of word problems I should focus on for exams? Answer: Yes, focus on age problems, distance problems, and mixture problems, as these are commonly tested in exams.
Now is the time to enhance your understanding and confidence! Dive into our practice MCQs on "Pair of Linear Equations - Word Problems" and test your skills. Remember, consistent practice is key to mastering this topic and excelling in your exams!
Q. A bakery sells cakes and cookies. If the total number of items is 150 and the number of cakes is twice the number of cookies, how many cakes are there?
A.
100
B.
50
C.
75
D.
25
Solution
Let the number of cookies be x. Then the number of cakes is 2x. The equation is x + 2x = 150. Solving gives 3x = 150, so x = 50. Therefore, cakes = 2x = 100.
Q. A bookstore sells novels and magazines. If the total number of books is 200 and the number of novels is 3 times the number of magazines, how many novels are there?
A.
150
B.
120
C.
75
D.
100
Solution
Let the number of magazines be x. Then the number of novels is 3x. The equation is x + 3x = 200. Solving gives 4x = 200, so x = 50. Therefore, novels = 3x = 150.
Q. A company produces pens and pencils. If the total production is 500 items and the number of pens is 4 times the number of pencils, how many pens are produced?
A.
400
B.
100
C.
200
D.
300
Solution
Let the number of pencils be x. Then the number of pens is 4x. The equation is x + 4x = 500. Solving gives 5x = 500, so x = 100. Therefore, pens = 4x = 400.
Q. A concert hall has 300 seats. If the number of reserved seats is 50 more than the number of general admission seats, how many reserved seats are there?
A.
125
B.
175
C.
100
D.
150
Solution
Let the number of general admission seats be x. Then the number of reserved seats is x + 50. The equation is x + (x + 50) = 300. Solving gives 2x + 50 = 300, so 2x = 250, x = 125. Therefore, reserved seats = x + 50 = 175.
Q. A farmer has chickens and cows. If there are 50 animals in total and the number of cows is 10 more than the number of chickens, how many cows are there?
A.
20
B.
30
C.
25
D.
15
Solution
Let the number of chickens be x. Then the number of cows is x + 10. The equation is x + (x + 10) = 50. Solving gives 2x + 10 = 50, so 2x = 40, x = 20. Therefore, cows = x + 10 = 30.
Q. A fruit seller has apples and oranges. If the total number of fruits is 80 and the number of apples is 3 times the number of oranges, how many apples are there?
A.
60
B.
30
C.
40
D.
50
Solution
Let the number of oranges be x. Then the number of apples is 3x. The equation is x + 3x = 80. Solving gives 4x = 80, so x = 20. Therefore, apples = 3x = 60.
Q. A school has 120 students. If the number of boys is twice the number of girls, how many boys are there?
A.
30
B.
40
C.
80
D.
60
Solution
Let the number of girls be x. Then the number of boys is 2x. The equation is x + 2x = 120. Solving gives 3x = 120, so x = 40. Therefore, boys = 2x = 80.