Please refer to **Case Study Chapter 3 Linear Equations Mathematics** with answers provided below. These case study based questions are expected to come in the upcoming Class 10 Mathematics examinations. We have provided case study questions class 10 maths for all chapters on our website as per the latest examination pattern issued by CBSE, NCERT, and KVS.

**Chapter 3 Linear Equations Case study Questions Class 10 Maths**

**I. The state governments revise fares from time to time based on various factors such as inflation, fuel price, demand from various quarters, etc. The government notifies different fares for different types of vehicles like Auto Rickshaws, Taxis, Radio Cab, etc The auto charges in a city comprise of a fixed charge together with the charge for the distance covered.****Study the following situations:****Situation-I: In city A, for a journey of 10 km, the charge paid is ₹ 75 and for a journey of 15 km, the charge paid is ₹ 110.****Situation-II: In city B, for a journey of 8 km, the charge paid is ₹ 91 and for a journey of 14 km, the charge paid is ₹ 145.**

**Question. A person travels a distance of 50 km. The amount he has to pay is **

(a) ₹ 155

(b) ₹ 255

(c) ₹ 355

(d) ₹ 455

**Answer**

C

**Question. The graphs of lines representing the conditions are **

**Answer**

C

**Question. What will a person have to pay for travelling a distance of 30 km?**

(a) ₹ 185

(b) ₹ 289

(c) ₹ 275

(d) ₹ 305

**Answer**

B

**Question. If the fixed charges of auto rickshaw be ` x and the running charges be ` y km/hr, the pair of linear equations representing the situation is **

(a) x + 10y = 110, x + 15y = 75

(b) x + 10y = 75, x + 15y = 110

(c) 10x + y = 110, 15x + y = 75

(d) 10x + y = 75, 15x + y = 110

**Answer**

A

**Question. What will a person have to pay for travelling a distance of 25 km? **

(a) ₹ 160

(b) ₹ 280

(c) ₹ 180

(d) ₹ 260

**Answer**

C

**II. Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq.m. Based on the above information, answer the following questions:**

**Question. The area of each bedroom and kitchen in the layout respectively is **

(a) 25 m, 35 m

(b) 15 m, 25 m

(c) 30 m, 35 m

(d) 25 m, 30 m

**Answer**

C

**Question. The cost of laying tiles in kitchen at the rate of ₹ 50 per sq m is **

(a) ₹ 1260

(b) ₹ 1750

(c) ₹ 1590

(d) ₹ 1810

**Answer**

B

**Question. The length of the outer boundary of the layout is **

(a) 35 m

(b) 54 m

(c) 42 m

(d) 60 m

**Answer**

B

**Question. The area of living room in the layout is **

(a) 55 sq. m

(b) 65 sq. m

(c) 75 sq. m

(d) 85 sq. m

**Answer**

C

**Question. The pair of linear equations in two variables from above situation is **

(a) x + y = 13, 2x + y = 19

(b) 2x + y = 13, x + y = 19

(c) x + 2y = 13, x – y = 19

(d) None of these

**Answer**

A

**III. Ankit and his friends went to a shop to purchase some daily use items. He purchased five copies and one book from the shop which cost him ₹ 500. His friends purchased the same copies and same books from other shop. If his friends purchased 10 copies and 3 books for ₹ 1300, then using variables ‘x’ and ‘y’ for the cost of one copy and one book respectively, answer the following questions:**

**Question. The above situations are representing a pair of linear equations which can be shown by drawing two lines in a plane. The following possibilities can happen. The two lines are **

(a) intersecting at one point

(b) parallel to each other

(c) coincident lines

(d) perpendicular to each other

**Answer**

A

**Question. The pair of linear equations shown by above situation are **

(a) consistent

(b) inconsistent

(c) dependent

(d) Both (a) and (c)

**Answer**

D

**Question. The algebraic representation of the above situation is given by the equations as **

(a) 5x + y = 500, 10x + 3y = 1300

(b) x + 5y = 500, 3x + 10y = 1300

(c) 5x – y = 500, 10x – 3y = 1300

(d) x – 5y = 500, 3x – 10y = 1300

**Answer**

A

**Question. Using above situations, the cost of one copy and one book separately is **

(a) ₹ 40, ₹ 300

(b) ₹ 60, ₹ 200

(c) ₹ 20, ₹ 400

(d) ₹ 60, ₹ 300

**Answer**

A

**Question. The above situations represent a pair of linear equations. The pair of linear equations show a/an **

(a) unique solution

(b) infinitely many solutions

(c) no solution

(d) None of the above

**Answer**

A

**IV.** **A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while 1/4 mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks.**

**Question. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got ? **

**Answer**

**Marks = 80 – 1/ 4 of 40 = 70**

**Question. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly? **

**Answer**

**No. of correct questions are 96 **

** Question. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks? **

**Answer**

**Here, x + y = 120 . x−1/4 y = 95**

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