Exam mathematics

Question 1

If the population/cost of a certain town/article, is P and annual increment rate is r%, then
1)After ‘t’ years population/cost=______
2)Before ‘t’ years population/cost =_______

Answer 1

1) P(1+(r/100))^t
2)P/(1+(r/100))^t

Question 2

Formula: If we change a number by x% & y% successively Then , net% change

Answer 2

[x+y+(xy/100)]%

Question 3

If the population of a town /cost of a article is P and it decreases/reduces at the rate of r% annually, then.
1)After ‘t’ years population/cost= ______
2)Before ‘t’ years population/cost = _______

Answer 3

1) P [1-(r/100)]^t
2) P/[1-(r/100)]^t

Question 4

Net % change of x%, y% and z% is

Answer 4

[(x+y+z)+ {(xy+yz+zx)/100}+{xyz/10000}]%

Question 5

If the present population of a town is P and the population increases or decreases at rate of R1%, R2% and R3% in first, second and third year respectively.
then the population of town after 3 years is

Answer 5

P[1+- (R1 /100)][1+- (R2 /100)][1+- (R3 /100)]
‘+’ is used when population increases and ‘-‘ is used when population decreases
NOTE - formula may be extended for n number of years.

Question 6

If an amount is increased by x% and then it is reduced by x % again , then percentage change will be a decrease of ____

Answer 6

x^2/100%

Question 7

If a number is increased by a% and then it is
decreased by b%, then resultant change in
percentage will be?

Answer 7

[a-b-(ab/100)]%

(Negative for decrease, Positive for increase)

Question 8

If the cost of an article is increased by A%, then how much to decrease the consumption of article, so that expenditure remains same is given by _____
OR
If the income of a man is A% more than another man, then income of another man is less in comparison to the 1st man by______

Answer 8

[{A/(100+A) }*100]%

Question 9

If the cost of an article is decreased by A%, then the increase in consumption of article to maintain the expenditure will be?
OR
If ‘x’ is A% less than ‘y’. then y is more than ‘x’ by _____

Answer 9

[{A/(100-A) }*100]%(increase)

Question 10

If the length of a rectangle is increase by a% and breadth is increased by b%, then the area of rectangle will increase by

Answer 10

[a+b+(ab/100)]%

Question 11

If the side of a square is increases by a % then its area will increase by

Answer 11

[2a+{a^2/100]%

Question 12

If the side of a square is decreased by a%, then
the area of square will decrease by

Answer 12

[-2a+{a^2/100]%
This formula is also applicable for circles where decrease % of radius is given.

Question 13

If the length, breadth and height of a cuboid are
increased by a%, b% and c% respectively, then,
Increase% in volume

Answer 13

[{a+b+c}+ {(ab+bc+ca)/100}+{abc/ (100)^2}]%

Question 14

If every side of cube or radius of sphere is increased by a%, then increase % in volume

Answer 14

[3a+(3a^2/100)+(a^3/100^2)]%

Question 15

If a% of a certain sum is taken by 1st man and b% of remaining sum is taken by 2nd man and finally c% of remaining sum is taken by 3rd man, then if
‘x’ rupee is the remaining amount then, Initial amount is ?

Answer 15

x{100/(100+a)}{100/(100+b)}*{100/(100+c)}

Question 16

On increasing/decreasing the cost of a certain article by x% , a person can buy ‘a’ kg article less/
more in ‘y’ rupees, then Increased/decreased cost of the article

Answer 16

xy / 100*a
and initial cost = xy/ (100 +-x)a
Note - [Negative sign when decreasing and positive sign
when increasing]

Question 17

If a person saves ‘R’ rupees after spending x% on
food, y% on cloth and z% on entertainment of his
income then. Monthly income =_______

Answer 17

{100/100-(x+y+z)}*R

Question 18

115