Question 1: Find all pairs of consecutive odd positive integers, both of which are smaller than , such that their sum is more than .

Answer:

Let the smaller odd positive number be .

Therefore the other odd positive number would be .

It is given that all pairs of consecutive odd positive integers, both of which are smaller than , such that their sum is more than .

and

and

Hence the required pars of odd integers are and .

Question 2: Find all pairs of consecutive odd natural number, both of which are larger than , such that their sum is less than .

Answer:

Let the smaller odd natural number be .

Therefore the other odd natural number would be .

It is given that all pairs of consecutive odd natural number, both of which are larger than , such that their sum is less than .

and

and

Hence the required pars of odd integers are and .

Question 3: Find all pairs of consecutive even positive integers, both of which are larger than , such that their sum is less than .

Answer:

Let the smaller even integer be .

Then, the other even integer will be .

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

and

and

Hence the required pars of odd integers are and .

Question 4: The marks scored by Rohit in two tests were and . Find the minimum marks he should score in the third test to have an average of at least marks.

Answer:

Let be the minimum marks Rohit needs to score in third test to have an average of at least .

Hence the minimum marks Rohit should score in the third test should be .

Question 5: A solution is to be kept between and . What is the range of temperature in degree Celsius, if the Celsius (C) / Fahrenheit (F) conversion formula is given by .

Answer:

Let the temperature of the solution in be

Hence the range of temperature in degree Celsius is and .

Question 6: A solution is to be kept between and . What is the range of temperature in degree Fahrenheit?

Answer:

Let the temperature of solution in to be

Hence the range of temperature in degree Fahrenheit is and

Question 7: To receive grade ‘A’ in a course, one must obtain an average of marks or more in five papers each of marks. If Shikha scored and marks in first four papers, find the minimum marks that she must score in the last paper to get grade ‘A’ in the course.

Answer:

Let be the minimum marks to be scored to get in course.

But you cannot score more than marks

Hence Shikha must score at least marks in the 5th paper to get grade in the course.

Question 8: A company manufactures cassettes and its cost and revenue functions for a week are and respectively, where is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?

Answer:

To earn profit, revenue must be greater then cost.

Therefore the company must sell more than cassettes in a week to make profit.

Question 9: The longest side of a triangle is three times the shortest side and the third side is cm shorter than the longest side if the perimeter of the triangles at least cm, Find the minimum length of the shortest-side.

Answer:

Let the shortest side of triangle be .

Therefore longest side is and the third side

Given Perimeter

Hence the minimum length of the shortest side is cm.

Question 10: How many litres of water will have to be added to litres of the solution of acid so that the resulting mixture will contain more than but less than acid content?

Answer:

Let liters of water is added to litres of solution.

Therefore the total quantity of solution

Total acid content in litres of mixture

Given resulting mixture will contain more than but less than acid content

and

Hence the water to be added should be greater than litres and less than litres.

Question 11: A solution of boric acid is to be diluted by adding boric acid solution to it. The resulting mixture is to be more than but less than boric acid. If there are litres of the solution, how many litres of solution will have to be added?

Answer:

Let litres of solution is added in the existing solution of of Boric acid.

Given resulting mixture is to be more than but less than boric acid.

and

and

and

Therefore the amount of boric acid solution that needs to be added needs to be more than litres and less than litres.

Question 12: The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between and . If the first two pH reading are and , find the range of pH value for the third reading that will result in the acidity level being normal.

Answer:

Let the third pH value be

Hence the range for the pH value for the third reading must be between and .