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
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
.
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:
Question 11: Make as a subject in the formula,
. Find
, when
.
Answer:
Question 12: Given:
(i) Make , the subject of the formula
(ii) Find , when
.
Answer:
Question 13:
(i) Make as the subject of the formula
(ii) Find , when
Answer:
Question 14: Let
(i) Find when
(ii) Find when
Answer:
Question 15: Let
(i) Make , the subject of the formula
(ii) Find , when
Answer:
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
Answer:
Question 17: Let ,
(i) Make the subject of the formula
(ii) Find , when
Answer:
Question 18: Let ,
(i) Make the subject of the formula
(ii) Find , when
Answer:
Question 19: Let ,
(i) Make the subject formula
(ii) Find , when
Answer:
Question 20: If , find
. Find
when
.
Answer:
Question 21: If , express
. Find
, when
.
Answer:
Question 22: Make the subject of
Answer: