KC Sinha Mathematics Solution Class 11 Chapter 13 Linear Inequalities Exercise 13.5

 Exercise 13.5

Page no 13.54 

Question 1

An electrician can be paid under two schemes as given below :

I : Rs. 500 and Rs. 70 per hour.

II : Rs. 120 per hour.

If the job takes $x$ hours, for what values of $x$ does the (i) Scheme I (ii) Schems II give the electrician the better wages.

Question 2

(i) The marks obtained by a student in two tests were 70 and 75.find the number of minimum marks he should get in the third test to have an average of at least 60 marks 

Page no 13.55

(ii) The marks obtained by a student of class XI in first terminal and second terminal are 62 and 48 respectively. Find the number of minimum marks he should get in the annual examination to have an average of at least 60 marks.

Question 3

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.

Question 4

In the first four examinations, each of 100 marks. Hamid got $94,73,72,84$ marks. If a final average greater than or equal to 80 and less than 90 is needed to obtain a final grade $B$ in a course, what range of marks on the fifth (last) examination will result in Hamid receiving ' $B$ ' in the course ?

Question 5

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?

Question 6

The longest side of a triangle is 3 times the shortest side and the third side is $2 \mathrm{~cm}$ shorter than the longest side. If the perimeter of the triangle is at least $61 \mathrm{~cm}$, find the minimum length of the shortest side.

Question 7

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

Question 8

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

Question 9

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

Question 10

In an experiment, a solution of hydrochloric acid is to be kept between $30^{\circ}$ and $35^{\circ}$ Celsius. What is the range of temperature in degree Fahrenheit if conversion formula is given by

$C=\frac{5}{9}(F-32) \text {, }$

Where $C$ and $F$ represent temperature in degree Celsius and degree Fahrenheit respectively.