Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ Question 21: Ravi obtained 70 and 75 marks in first two-unit test. Find the minimum marks he should get in the third test to have an average of at least 60 marks. Solution 21: Let x be the marks obtained by Ravi in the third unit test. Since the student should have an average of at least 60 marks, 70 75 x 60 3 145 x 180 x 180 145 x 35 Thus, the student must obtain a minimum of 35 marks to have an average of at least 60 marks. Question 22: 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. Solution 22: Let x be the marks obtained by Sunita in the fifth examination. In order to receive grade ‘A’ in the course, she must obtain an average of 90 marks or more in five examinations. Therefore, 87 92 94 95 x 90 5 368 x 90 5 368 x 450 x 450 368 x 82 Thus, Sunita must obtain greater than or equal to 82 marks in the fifth examination. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ Question 23: Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than **11**. Solution 23: Let x be the smaller of the two consecutive odd positive integers. Then, the other integer is Since both the integers are smaller than 10, x 2 10 x 10 2 x8 .....i Also, the sum of the two integers is more than **11**. x x 2 **11** 2x 2 **11** 2x **11** 2 2x 9 x 9 2 x 4.5 .......ii From (i) and (ii), we obtain Since x is an odd number, x can take the values, 5 and 7. Thus, the required possible pairs are (5, 7) and (7, 9). x 2. Question 24: Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23. Solution 24: Let x be the smaller of the two consecutive even positive integers. Then, the other integer is . Since both the integers are larger than 5, x 2 x 5........ 1 Also, the sum of the two integers is less than 23 x x 2 23 2x 2 23 2x 23 2 2x 21 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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