Question 22 of 40intermediate🔧 ApplyNumerical4 marks

To receive Grade 'A' in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain in fifth examination to get grade 'A' in the course.

Correct Answer

Sunita must obtain a minimum of 82 marks in the fifth examination to get Grade 'A' in the course.

Exercise: EXERCISE 5.1 | Q: 22 | (Page Page 8)
For More Understanding

Explanation

This question is from the Linear Inequalities chapter (Chapter 5) of NCERT Class 11 Mathematics. It tests the student's ability to formulate and solve an inequality based on a real-life situation. The question is similar to Example 7 in the textbook, where a student needs to find minimum marks to achieve a certain average. The key concept is understanding that 'average of 90 marks or more' translates to the inequality ≥\geq 90, and solving for the unknown marks in the fifth examination.

Solution Steps

  1. Step 1: Let x be the marks obtained by Sunita in the fifth examination.

  2. Step 2: Calculate the total marks in first four examinations: 87 + 92 + 94 + 95 = 368

  3. Step 3: Total marks in five examinations = 368 + x

  4. Step 4: For Grade 'A', average must be 90 or more: (368 + x)/5 ≥\geq 90

  5. Step 5: Multiply both sides by 5: 368 + x ≥\geq 450

  6. Step 6: Subtract 368 from both sides: x ≥\geq 450 - 368, which gives x ≥\geq 82

  7. Step 7: Therefore, minimum marks required in fifth examination = 82 marks.

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