Question 1: Frame a formula for each of the following statements:

(i) The area of a rectangle is equal to the product of its length and breadth

(ii) The area of a triangle is half the product of its base and height

(iii) The volume of the cone is one third the product of , square of the radius and height

(iv) The perimeter of the rectangle is twice the sum of its length and breadth

(v) The perimeter of a square is four times it size

(vi) The distance through which the body falls freely under gravity is times the square of the time

(vii) The reciprocal of focal length is equal to the sum of reciprocals of the object distance and the image distance

(viii) years ago, a man whose present age is years was three times as old as his son, whose present age is years

(ix) Two digit number having as ten’s digit and as units’s digit is times the sum of the digits

(x) The number of diagonals that can be drawn from one vertex of an -side polygon to all other vertices is less than

Question 2: A workman is paid for each day he works and fined for each day he is absent. If he works for days in a month of days, find the expression of his total earnings in rupees.

Answer:

Question 3: A purse contains notes of each, notes of each, coins of paisa each and coins of paisa each. Find the total money in .

Answer:

Question 4: A shopkeeper buys kg. of rice at per kg and another kg of rice at per kg. He mixes the two quantities and sells the mixture at per kg. Find the expression of his (i) total profit and (ii) profit per cent.

Answer:

Total cost

Total Sale

(i) Total profit

(ii) Profit percentage

Question 5: A man cycles for hours at km per hour and for another hours at km per hour. Find his average speed for the whole journey.

Answer:

Question 6: The average age of boys in a class is years. A new boy of age years joins the class. Find the present average age .

Answer:

Question 7: A cricketer has an average score of runs per innings in innings and an average of runs per innings in innings. Find the average score per innings.

Answer:

Question 8: In a class of children, each one of y children pays and each of the remaining pays for a charity show. Find the total amount in rupees.

Answer:

Question 9: A shopkeeper marks each article at and gives discount on the marked price. If the cost price of an article , find the formula for profit . Find P when and .

Answer:

Question 10: The hiring charges of a taxi were plus per km for distances traveled beyond km. If the distance traveled is km, write a formula for the hiring charges.

Answer:

If

Question 11: Make as a subject in the formula, . Find , when and .

Answer:

Question 12: Given:

(i) Make , the subject of the formula

(ii) Find , when and .

Answer:

(i)

(ii) when and

Question 13: Given:

(i) Make as the subject of the formula

(ii) Find , when and

Answer:

(i)

(ii) When and

Question 14: Let

(i) Find when and

(ii) Find when and

Answer:

(i)

(ii)

Question 15: Let

(i) Make , the subject of the formula

(ii) Find , when and

Answer:

(i)

(ii)

Question 16: The volume of a hollow cylindrical pipe with outer radius , inner radius and length is given by the formula, .

(i) Make the subject of the formula

(ii) Find , when and

Answer:

(i)

(ii)

Question 17: Let ,

(i) Make the subject of the formula

(ii) Find , when and

Answer:

(i)

(ii)

Question 18: Let ,

(i) Make the subject of the formula

(ii) Find , when and

Answer:

(i)

(ii)

Question 19: Let ,

(i) Make the subject formula

(ii) Find , when and

Answer:

(i)

(ii)

Question 20: If , find in terms of and . Find when and .

Answer:

Question 21: If , express in terms of and . Find , when and .

Answer:

Question 22: Make the subject of

Answer: