RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 15. Linear Inequations

Subject: Maths - Class 11th

Q. No. 4 of Exercise 15.4

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4

The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.

Given: Marks scored by Rohit in two tests are 65 and 70.


To find Minimum marks in the third test to make an average of at least 65 marks.


Let marks in the third test be x.


According to the question, we need to find minimum x for which the average of all three papers would be at least 65 marks.


That is,


Average marks in three papers ≥ 65 …(i)


Now, we know that average is given as



So, an average of the marks in these three tests is given by






Substituting this value of average in the inequality (i), we get



⇒ (135 + x) ≥ 65 × 3


⇒ (135 + x) ≥ 195


⇒ x ≥ 195 – 135


⇒ x ≥ 60


This inequality means that Rohit should score at least 60 marks in his third test to have an average of at least 65 marks.


So, the minimum marks to get an average of 65 marks is 60.


Thus, the minimum marks required in the third test is 60.


Chapter Exercises

Exercise 15.3
Exercise 15.4
Exercise 15.1
Exercise 15.2
Exercise 15.5
Exercise 15.6
Very Short Answer
MCQ

More Exercise Questions

1

Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.
2

Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.
3

Find all pairs of consecutive even positive integers, both of which are larger than 5, such that their sum is less than 23.
4

The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.
5

A solution is to be kept between 86o and 95oF. What is the range of temperature in degree Celsius, if the Celsius (C)/Fahrenheit (F) conversion formula is given by

6

A solution is to be kept between 30oC and 35oC. What is the range of temperature in degree Fahrenheit?
7

To receive grade ‘A’ in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four papers, find the minimum marks that she must score in the last paper to get grade ‘A’ in the course.
8

A company manufactures cassettes and its cost and revenue functions for a week are and R = 2x respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?
9

The longest side of a triangle is three times the shortest side, and the third side is 2 cm shorter than the longest side if the perimeter of the triangle at least 61 cm, Find the minimum length of the shortest-side.
10

How many liters of water will have to be added to 1125 liters of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
11

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 liters of the 8% solution, how many liters of 2% solution will have to be added?
12

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading is 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level is normal.

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