text: # Case study Chapter 4(Determinant)
  
  Case study 4:– Read the following and answer the question(Case study problem determinant 4)
  
  On the occasion of children’s day. Class teacher of class XII shri singh, decided to donate some money to students of class XII.
  
  If there were 8 studens less, every one would have got ₹10 more, however if there were 16 students more, everyone would have got ₹10 less.
  
  (i) If number of students in class be x  and Shri Singh has to decided to donate ₹y to each student, then the information provided in problem may be written in system of linear equation as
  
  (a) 5x + 4y = 40, 5x – 8y = -80
  
  (b)  x – y = 40, 2x – 3y = 80
  
  (c) 5x – 4y = 40, 5x – 8y = -80
  
  (d) 8x + 10y = 40, 16x – 10y = 80
  
  (ii) System of linear equations obtained in (i) may be written in matrix equation as
  
  (a)
  
  (b)
  
  (c)
  
  (d)
  
  (iii) If AX = B, where A, X, B are matrix, then X should be
  
  (a) X = AB                              (b)
  
  (c)                  (d)
  
  (iv) If then is
  
  (a)
  
  (b)
  
  (c)
  
  (d)
  
  (v) The number of students in class XII and amount distributed by Shri Singh respectively is
  
  (a) 30, ₹ 32                         (b) 30, ₹30
  
  (c) 30,₹32                            (d) 32 ₹32
  
  From question
  
  (x – 8)(y + 10) = xy
  
  ⇒ x.y + 10x – 8y – 80 = x.y
  
  ⇒ 10x – 8y = 80
  
  ⇒ 5x – 4y = 40 —–(i)
  
  Also,
  
  (x + 16)(y – 10) = xy
  
  ⇒ x.y – 10x + 16y – 160 = x.y
  
  ⇒ 10x – 16y = -160
  
  ⇒ 5x – 8y = -80 —–(ii)
  
  We have system of linear equations,
  
  5x – 4y = 40 —–(i)
  
  5x – 8y = -80 —–(ii)
  
  We can write matrix system as
  
  We have
  
  AX = B
  
  Pre multiplying both sides, we have
  
  We have
  
  ⇒ |A| = -40 + 20 = -20 ≠ 0
  
  NOW,
  
  ⇒  x  = 32, and  y = 30
  
  ## Some other Case study problem
  
  Case study 1:–  Read the following and answer the questions(Case study problem determinant 1)
  
  Three friends Rahul, Ravi and Rakesh went to a vegetable market to purchase vegetable. From a vegetable shop Rahul purchased 1 kg of each potato, onion and Brinjal for a total of ₹ 21. Ravi purchased 4 kg of potato, 3 kg of onion and 2 kg of Brijal for ₹ 60 while Rakesh purchased 6 kg potato, 2 kg onion and 3 kg Brinjal for ₹70
  
  Case study 2:- Read the following and answer the question(Case study problem determinant 2)
  
  Reshma wants to donate a rectangular plot of land for a school of her village. When she was asked by construction agency to give dimensions of the plot, she said that if its length is decreased by 50 m and breadth is increased by 50m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20m, then its area will decreased by 5300 m².
  
  Case study 3:– Read the following and answer the question(Case study problem determinant 3 )
  
  The monthly incomes of two sister Reshma and Ritam are in the ratio 3:4 and their monthly expenditures are in the ratio 5;7. Each sister saves ₹ 15,000 per month.
explanation: The document contains a case study problem related to determinants and linear equations. It presents a scenario where a teacher, Shri Singh, decides to donate money to students in a class. The problem provides conditions based on the number of students and the amount of money each student would receive, and it asks a series of questions related to forming and solving a system of linear equations.
  
  The document includes multiple questions and their corresponding answers, covering the formation of linear equations, matrix representation, and solving for the number of students and the amount of money distributed.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Case study Chapter 4(Determinant)
  
  Case study 4:– Read the following and answer the question(Case study problem determinant 4)
  
  On the occasion of children’s day. Class teacher of class XII shri singh, decided to donate some money to students of class XII.
  
  If there were 8 studens less, every one would have got ₹10 more, however if there were 16 students more, everyone would have got ₹10 less.
  
  (i) If number of students in class be x  and Shri Singh has to decided to donate ₹y to each student, then the information provided in problem may be written in system of linear equation as
  
  (a) 5x + 4y = 40, 5x – 8y = -80
  
  (b)  x – y = 40, 2x – 3y = 80
  
  (c) 5x – 4y = 40, 5x – 8y = -80
  
  (d) 8x + 10y = 40, 16x – 10y = 80
  
  (ii) System of linear equations obtained in (i) may be written in matrix equation as
  
  (a)
  
  (b)
  
  (c)
  
  (d)
  
  (iii) If AX = B, where A, X, B are matrix, then X should be
  
  (a) X = AB                              (b)
  
  (c)                  (d)
  
  (iv) If then is
  
  (a)
  
  (b)
  
  (c)
  
  (d)
  
  (v) The number of students in class XII and amount distributed by Shri Singh respectively is
  
  (a) 30, ₹ 32                         (b) 30, ₹30
  
  (c) 30,₹32                            (d) 32 ₹32
  
  From question
  
  (x – 8)(y + 10) = xy
  
  ⇒ x.y + 10x – 8y – 80 = x.y
  
  ⇒ 10x – 8y = 80
  
  ⇒ 5x – 4y = 40 —–(i)
  
  Also,
  
  (x + 16)(y – 10) = xy
  
  ⇒ x.y – 10x + 16y – 160 = x.y
  
  ⇒ 10x – 16y = -160
  
  ⇒ 5x – 8y = -80 —–(ii)
  
  We have system of linear equations,
  
  5x – 4y = 40 —–(i)
  
  5x – 8y = -80 —–(ii)
  
  We can write matrix system as
  
  We have
  
  AX = B
  
  Pre multiplying both sides, we have
  
  We have
  
  ⇒ |A| = -40 + 20 = -20 ≠ 0
  
  NOW,
  
  ⇒  x  = 32, and  y = 30
  
  ## Some other Case study problem
  
  Case study 1:–  Read the following and answer the questions(Case study problem determinant 1)
  
  Three friends Rahul, Ravi and Rakesh went to a vegetable market to purchase vegetable. From a vegetable shop Rahul purchased 1 kg of each potato, onion and Brinjal for a total of ₹ 21. Ravi purchased 4 kg of potato, 3 kg of onion and 2 kg of Brijal for ₹ 60 while Rakesh purchased 6 kg potato, 2 kg onion and 3 kg Brinjal for ₹70
  
  Case study 2:- Read the following and answer the question(Case study problem determinant 2)
  
  Reshma wants to donate a rectangular plot of land for a school of her village. When she was asked by construction agency to give dimensions of the plot, she said that if its length is decreased by 50 m and breadth is increased by 50m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20m, then its area will decreased by 5300 m².
  
  Case study 3:– Read the following and answer the question(Case study problem determinant 3 )
  
  The monthly incomes of two sister Reshma and Ritam are in the ratio 3:4 and their monthly expenditures are in the ratio 5;7. Each sister saves ₹ 15,000 per month.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a case study problem related to determinants and linear equations. It presents a scenario where a teacher, Shri Singh, decides to donate money to students in a class. The problem provides conditions based on the number of students and the amount of money each student would receive, and it asks a series of questions related to forming and solving a system of linear equations.
  
  The document includes multiple questions and their corresponding answers, covering the formation of linear equations, matrix representation, and solving for the number of students and the amount of money distributed.
  
  Label: multiple-question-and-answer